TSTP Solution File: SYN067-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN067-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:53:30 EDT 2022
% Result : Unsatisfiable 0.67s 0.72s
% Output : Proof 1.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN067-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 01:44:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.67/0.72 % SZS status Unsatisfiable
% 0.67/0.72 % SZS output start Proof
% 0.67/0.72 tff(big_r_type, type, (
% 0.67/0.72 big_r: ( $i * $i ) > $o)).
% 0.67/0.72 tff(f5_type, type, (
% 0.67/0.72 f5: $i > $i)).
% 0.67/0.72 tff(c4_type, type, (
% 0.67/0.72 c4: $i)).
% 0.67/0.72 tff(big_p_type, type, (
% 0.67/0.72 big_p: $i > $o)).
% 0.67/0.72 tff(c3_type, type, (
% 0.67/0.72 c3: $i)).
% 0.67/0.72 tff(f2_type, type, (
% 0.67/0.72 f2: $i > $i)).
% 0.67/0.72 tff(c2_type, type, (
% 0.67/0.72 c2: $i)).
% 0.67/0.72 tff(f1_type, type, (
% 0.67/0.72 f1: $i > $i)).
% 0.67/0.72 tff(f6_type, type, (
% 0.67/0.72 f6: $i > $i)).
% 0.67/0.72 tff(c1_type, type, (
% 0.67/0.72 c1: $i)).
% 0.67/0.72 tff(f4_type, type, (
% 0.67/0.72 f4: $i > $i)).
% 0.67/0.72 tff(a_type, type, (
% 0.67/0.72 a: $i)).
% 0.67/0.72 tff(f3_type, type, (
% 0.67/0.72 f3: $i > $i)).
% 0.67/0.72 tff(1,assumption,(~big_r(c2, f1(c2))), introduced(assumption)).
% 0.67/0.72 tff(2,assumption,(~big_p(c1)), introduced(assumption)).
% 0.67/0.72 tff(3,assumption,(~big_r(c4, f1(c4))), introduced(assumption)).
% 0.67/0.72 tff(4,assumption,(~big_p(c2)), introduced(assumption)).
% 0.67/0.72 tff(5,assumption,(~big_p(c4)), introduced(assumption)).
% 0.67/0.72 tff(6,assumption,(~big_p(f4(c2))), introduced(assumption)).
% 0.67/0.72 tff(7,plain,
% 0.67/0.72 (^[X7: $i, X1: $i] : refl((big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) <=> (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)))),
% 0.67/0.72 inference(bind,[status(th)],[])).
% 0.67/0.72 tff(8,plain,
% 0.67/0.72 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) <=> ![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.67/0.72 inference(quant_intro,[status(thm)],[7])).
% 0.67/0.72 tff(9,plain,
% 0.67/0.72 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) <=> ![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(10,plain,
% 0.67/0.72 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) <=> ($false | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)))), rewrite(($false | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) <=> (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))), (((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) <=> (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))))),
% 0.67/0.72 inference(bind,[status(th)],[])).
% 0.67/0.72 tff(11,plain,
% 0.67/0.72 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) <=> ![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.67/0.72 inference(quant_intro,[status(thm)],[10])).
% 0.67/0.72 tff(12,plain,
% 0.67/0.72 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_p(f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) | big_p(f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))))),
% 0.67/0.72 inference(bind,[status(th)],[])).
% 0.67/0.72 tff(13,plain,
% 0.67/0.72 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.67/0.72 inference(quant_intro,[status(thm)],[12])).
% 0.67/0.72 tff(14,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.67/0.72 tff(15,plain,
% 0.67/0.72 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.67/0.72 tff(16,plain,
% 0.67/0.72 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.67/0.72 tff(17,plain,
% 0.67/0.72 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.67/0.72 tff(18,plain,(
% 0.67/0.72 ![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.67/0.72 inference(skolemize,[status(sab)],[17])).
% 0.67/0.72 tff(19,plain,
% 0.67/0.72 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.67/0.72 tff(20,plain,
% 0.67/0.72 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_p(f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_p(f2(c4)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(21,plain,
% 0.67/0.72 ((big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | big_p(c4)) <=> (big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_p(f2(c4)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(22,plain,
% 0.67/0.72 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | big_p(c4))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_p(f2(c4))))),
% 0.67/0.72 inference(monotonicity,[status(thm)],[21])).
% 0.67/0.72 tff(23,plain,
% 0.67/0.72 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | big_p(c4))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_p(f2(c4)))),
% 0.67/0.72 inference(transitivity,[status(thm)],[22, 20])).
% 0.67/0.72 tff(24,plain,
% 0.67/0.72 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | big_p(c4))),
% 0.67/0.72 inference(quant_inst,[status(thm)],[])).
% 0.67/0.72 tff(25,plain,
% 0.67/0.72 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_p(f2(c4))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.67/0.72 tff(26,plain,
% 0.67/0.72 (big_p(f4(c2)) | big_p(f2(c4))),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[25, 19, 5, 4])).
% 0.67/0.72 tff(27,plain,
% 0.67/0.72 (big_p(f2(c4))),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[26, 6])).
% 0.67/0.72 tff(28,plain,
% 0.67/0.72 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(c2) | big_p(f4(c2)) | big_p(f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | big_p(c2) | big_p(f4(c2)) | big_p(f2(c2)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(29,plain,
% 0.67/0.72 ((big_p(f4(c2)) | big_p(c2) | big_p(f2(c2)) | big_p(c2)) <=> (big_p(c2) | big_p(f4(c2)) | big_p(f2(c2)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(30,plain,
% 0.67/0.72 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(f4(c2)) | big_p(c2) | big_p(f2(c2)) | big_p(c2))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(c2) | big_p(f4(c2)) | big_p(f2(c2))))),
% 0.67/0.73 inference(monotonicity,[status(thm)],[29])).
% 0.67/0.73 tff(31,plain,
% 0.67/0.73 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(f4(c2)) | big_p(c2) | big_p(f2(c2)) | big_p(c2))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | big_p(c2) | big_p(f4(c2)) | big_p(f2(c2)))),
% 0.67/0.73 inference(transitivity,[status(thm)],[30, 28])).
% 0.67/0.73 tff(32,plain,
% 0.67/0.73 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(f4(c2)) | big_p(c2) | big_p(f2(c2)) | big_p(c2))),
% 0.67/0.73 inference(quant_inst,[status(thm)],[])).
% 0.67/0.73 tff(33,plain,
% 0.67/0.73 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | big_p(c2) | big_p(f4(c2)) | big_p(f2(c2))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.67/0.73 tff(34,plain,
% 0.67/0.73 (big_p(f4(c2)) | big_p(f2(c2))),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[33, 19, 4])).
% 0.67/0.73 tff(35,plain,
% 0.67/0.73 (big_p(f2(c2))),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[34, 6])).
% 0.67/0.73 tff(36,plain,
% 0.67/0.73 (^[X7: $i, X1: $i] : refl((big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) <=> (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))))),
% 0.67/0.73 inference(bind,[status(th)],[])).
% 0.67/0.73 tff(37,plain,
% 0.67/0.73 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.67/0.73 inference(quant_intro,[status(thm)],[36])).
% 0.67/0.73 tff(38,plain,
% 0.67/0.73 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(39,plain,
% 0.67/0.73 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) <=> ($false | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))))), rewrite(($false | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) <=> (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))), (((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) <=> (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))))),
% 0.67/0.73 inference(bind,[status(th)],[])).
% 0.67/0.73 tff(40,plain,
% 0.67/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.67/0.73 inference(quant_intro,[status(thm)],[39])).
% 0.67/0.73 tff(41,plain,
% 0.67/0.73 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) | big_p(f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))))),
% 0.67/0.73 inference(bind,[status(th)],[])).
% 0.67/0.73 tff(42,plain,
% 0.67/0.73 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.67/0.73 inference(quant_intro,[status(thm)],[41])).
% 0.67/0.73 tff(43,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_7')).
% 0.67/0.73 tff(44,plain,
% 0.67/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.67/0.73 tff(45,plain,
% 0.67/0.73 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.67/0.73 tff(46,plain,
% 0.67/0.73 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.67/0.73 tff(47,plain,(
% 0.67/0.73 ![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.67/0.73 inference(skolemize,[status(sab)],[46])).
% 0.67/0.73 tff(48,plain,
% 0.67/0.73 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.67/0.73 tff(49,plain,
% 0.67/0.73 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(c4, f1(c4)))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(50,plain,
% 0.67/0.73 ((big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(c4, f1(c4))) <=> (big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(c4, f1(c4)))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(51,plain,
% 0.67/0.73 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(c4, f1(c4))))),
% 0.67/0.73 inference(monotonicity,[status(thm)],[50])).
% 0.67/0.73 tff(52,plain,
% 0.67/0.73 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(c4, f1(c4)))),
% 0.67/0.73 inference(transitivity,[status(thm)],[51, 49])).
% 0.67/0.73 tff(53,plain,
% 0.67/0.73 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(c4, f1(c4)))),
% 0.67/0.73 inference(quant_inst,[status(thm)],[])).
% 0.67/0.73 tff(54,plain,
% 0.67/0.73 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(c4, f1(c4))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.67/0.73 tff(55,plain,
% 0.67/0.73 (big_p(f4(c2)) | big_r(c4, f1(c4))),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[54, 48, 5, 4])).
% 0.67/0.73 tff(56,plain,
% 0.67/0.73 (big_p(f4(c2))),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[55, 3])).
% 0.67/0.73 tff(57,plain,
% 0.67/0.73 (^[X7: $i, X1: $i] : refl((big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7))) <=> (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(58,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[57])).
% 0.77/0.73 tff(59,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(60,plain,
% 0.77/0.73 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7))) <=> ($false | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7))))), rewrite(($false | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7))) <=> (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))), (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7))) <=> (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(61,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[60])).
% 0.77/0.73 tff(62,plain,
% 0.77/0.73 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) | big_r(X1, f3(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(63,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[62])).
% 0.77/0.73 tff(64,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_8')).
% 0.77/0.73 tff(65,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.77/0.73 tff(66,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.77/0.73 tff(67,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.77/0.73 tff(68,plain,(
% 0.77/0.73 ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(skolemize,[status(sab)],[67])).
% 0.77/0.73 tff(69,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.77/0.73 tff(70,plain,
% 0.77/0.73 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4)))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(71,plain,
% 0.77/0.73 ((big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4))) <=> (big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4)))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(72,plain,
% 0.77/0.73 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4))))),
% 0.77/0.73 inference(monotonicity,[status(thm)],[71])).
% 0.77/0.73 tff(73,plain,
% 0.77/0.73 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4)))),
% 0.77/0.73 inference(transitivity,[status(thm)],[72, 70])).
% 0.77/0.73 tff(74,plain,
% 0.77/0.73 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4)))),
% 0.77/0.73 inference(quant_inst,[status(thm)],[])).
% 0.77/0.73 tff(75,plain,
% 0.77/0.73 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.77/0.73 tff(76,plain,
% 0.77/0.73 (big_r(c4, f3(c4)) | big_r(c4, f1(c4))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[75, 69, 5])).
% 0.77/0.73 tff(77,plain,
% 0.77/0.73 (big_r(c4, f3(c4))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[76, 3])).
% 0.77/0.73 tff(78,plain,
% 0.77/0.73 (^[X7: $i, X1: $i] : refl((big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7))) <=> (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(79,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[78])).
% 0.77/0.73 tff(80,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(81,plain,
% 0.77/0.73 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7))) <=> ($false | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7))))), rewrite(($false | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7))) <=> (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))), (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7))) <=> (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(82,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[81])).
% 0.77/0.73 tff(83,plain,
% 0.77/0.73 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) | big_r(f3(X1), f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(84,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[83])).
% 0.77/0.73 tff(85,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_9')).
% 0.77/0.73 tff(86,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.77/0.73 tff(87,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.77/0.73 tff(88,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.77/0.73 tff(89,plain,(
% 0.77/0.73 ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(skolemize,[status(sab)],[88])).
% 0.77/0.73 tff(90,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.77/0.73 tff(91,plain,
% 0.77/0.73 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4)))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(92,plain,
% 0.77/0.73 ((big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4))) <=> (big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4)))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(93,plain,
% 0.77/0.73 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4))))),
% 0.77/0.73 inference(monotonicity,[status(thm)],[92])).
% 0.77/0.73 tff(94,plain,
% 0.77/0.73 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4)))),
% 0.77/0.73 inference(transitivity,[status(thm)],[93, 91])).
% 0.77/0.73 tff(95,plain,
% 0.77/0.73 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4)))),
% 0.77/0.73 inference(quant_inst,[status(thm)],[])).
% 0.77/0.73 tff(96,plain,
% 0.77/0.73 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.77/0.73 tff(97,plain,
% 0.77/0.73 (big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[96, 90, 5])).
% 0.77/0.73 tff(98,plain,
% 0.77/0.73 (big_r(f3(c4), f4(c4))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[97, 3])).
% 0.77/0.73 tff(99,assumption,(~big_r(c2, f3(c2))), introduced(assumption)).
% 0.77/0.73 tff(100,plain,
% 0.77/0.73 (^[X7: $i, X1: $i] : refl((big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1))) <=> (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(101,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[100])).
% 0.77/0.73 tff(102,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(103,plain,
% 0.77/0.73 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1))) <=> ($false | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1))))), rewrite(($false | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1))) <=> (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))), (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1))) <=> (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(104,plain,
% 0.77/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[103])).
% 0.77/0.73 tff(105,plain,
% 0.77/0.73 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_p(f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) | big_r(X1, f3(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))))),
% 0.77/0.74 inference(bind,[status(th)],[])).
% 0.77/0.74 tff(106,plain,
% 0.77/0.74 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.77/0.74 inference(quant_intro,[status(thm)],[105])).
% 0.77/0.74 tff(107,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.77/0.74 tff(108,plain,
% 0.77/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.77/0.74 tff(109,plain,
% 0.77/0.74 (![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.77/0.74 tff(110,plain,
% 0.77/0.74 (![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.77/0.74 tff(111,plain,(
% 0.77/0.74 ![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.77/0.74 inference(skolemize,[status(sab)],[110])).
% 0.77/0.74 tff(112,plain,
% 0.77/0.74 (![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[111, 101])).
% 0.77/0.74 tff(113,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c2)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(114,plain,
% 0.77/0.74 ((big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(c2, f3(c2))) <=> (big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c2)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(115,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(c2, f3(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c2))))),
% 0.77/0.74 inference(monotonicity,[status(thm)],[114])).
% 0.77/0.74 tff(116,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(c2, f3(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c2)))),
% 0.77/0.74 inference(transitivity,[status(thm)],[115, 113])).
% 0.77/0.74 tff(117,plain,
% 0.77/0.74 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(c2, f3(c2)))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(118,plain,
% 0.77/0.74 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c2))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.77/0.74 tff(119,plain,
% 0.77/0.74 (big_p(f2(c2))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[118, 112, 4, 99])).
% 0.77/0.74 tff(120,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_p(f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_p(f2(c4)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(121,plain,
% 0.77/0.74 ((big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(c2, f3(c2))) <=> (big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_p(f2(c4)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(122,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(c2, f3(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_p(f2(c4))))),
% 0.77/0.74 inference(monotonicity,[status(thm)],[121])).
% 0.77/0.74 tff(123,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(c2, f3(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_p(f2(c4)))),
% 0.77/0.74 inference(transitivity,[status(thm)],[122, 120])).
% 0.77/0.74 tff(124,plain,
% 0.77/0.74 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(c2, f3(c2)))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(125,plain,
% 0.77/0.74 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_p(f2(c4))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.77/0.74 tff(126,plain,
% 0.77/0.74 (big_p(f2(c4))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[125, 112, 5, 4, 99])).
% 0.77/0.74 tff(127,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(c4, f1(c4)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(128,plain,
% 0.77/0.74 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(c4, f1(c4)))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(129,plain,
% 0.77/0.74 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(c4, f1(c4))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.77/0.74 tff(130,plain,
% 0.77/0.74 (big_r(c2, f3(c2)) | big_r(c4, f1(c4))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[129, 69, 5, 4])).
% 0.77/0.74 tff(131,plain,
% 0.77/0.74 (big_r(c4, f1(c4))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[130, 99])).
% 0.77/0.74 tff(132,plain,
% 0.77/0.74 (^[X7: $i, X1: $i] : refl((big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7))) <=> (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7))))),
% 0.77/0.74 inference(bind,[status(th)],[])).
% 0.77/0.74 tff(133,plain,
% 0.77/0.74 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.77/0.74 inference(quant_intro,[status(thm)],[132])).
% 0.77/0.74 tff(134,plain,
% 0.77/0.74 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(135,plain,
% 0.77/0.74 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7))) <=> ($false | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7))))), rewrite(($false | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7))) <=> (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))), (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7))) <=> (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))))),
% 0.77/0.74 inference(bind,[status(th)],[])).
% 0.77/0.74 tff(136,plain,
% 0.77/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.77/0.74 inference(quant_intro,[status(thm)],[135])).
% 0.77/0.74 tff(137,plain,
% 0.77/0.74 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_r(X1, f3(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))))),
% 0.77/0.74 inference(bind,[status(th)],[])).
% 0.77/0.74 tff(138,plain,
% 0.77/0.74 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.77/0.74 inference(quant_intro,[status(thm)],[137])).
% 0.77/0.74 tff(139,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_14')).
% 0.77/0.74 tff(140,plain,
% 0.77/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.77/0.74 tff(141,plain,
% 0.77/0.74 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.77/0.74 tff(142,plain,
% 0.77/0.74 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.77/0.74 tff(143,plain,(
% 0.77/0.74 ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.77/0.74 inference(skolemize,[status(sab)],[142])).
% 0.77/0.74 tff(144,plain,
% 0.77/0.74 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[143, 133])).
% 0.77/0.74 tff(145,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(f1(c4), f2(c4)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(146,plain,
% 0.77/0.74 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(f1(c4), f2(c4)))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(147,plain,
% 0.77/0.74 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(f1(c4), f2(c4))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.77/0.74 tff(148,plain,
% 0.77/0.74 (big_r(c2, f3(c2)) | big_r(f1(c4), f2(c4))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[147, 144, 5, 4])).
% 0.77/0.74 tff(149,plain,
% 0.77/0.74 (big_r(f1(c4), f2(c4))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[148, 99])).
% 0.77/0.74 tff(150,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(c4, f3(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(c4, f3(c4)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(151,plain,
% 0.77/0.74 ((big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(c2, f1(c2))) <=> (big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(c4, f3(c4)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(152,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(c4, f3(c4))))),
% 0.77/0.74 inference(monotonicity,[status(thm)],[151])).
% 0.77/0.74 tff(153,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(c4, f3(c4)))),
% 0.77/0.74 inference(transitivity,[status(thm)],[152, 150])).
% 0.77/0.74 tff(154,plain,
% 0.77/0.74 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(c2, f1(c2)))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(155,plain,
% 0.77/0.74 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(c4, f3(c4))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.77/0.74 tff(156,plain,
% 0.77/0.74 (big_r(c4, f3(c4))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[155, 69, 5, 4, 1])).
% 0.77/0.74 tff(157,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(f3(c4), f4(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(f3(c4), f4(c4)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(158,plain,
% 0.77/0.74 ((big_p(c4) | big_p(c2) | big_r(f3(c4), f4(c4)) | big_r(c2, f1(c2))) <=> (big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(f3(c4), f4(c4)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(159,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_p(c2) | big_r(f3(c4), f4(c4)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(f3(c4), f4(c4))))),
% 0.77/0.74 inference(monotonicity,[status(thm)],[158])).
% 0.77/0.74 tff(160,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_p(c2) | big_r(f3(c4), f4(c4)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(f3(c4), f4(c4)))),
% 0.77/0.74 inference(transitivity,[status(thm)],[159, 157])).
% 0.77/0.74 tff(161,plain,
% 0.77/0.74 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_p(c2) | big_r(f3(c4), f4(c4)) | big_r(c2, f1(c2)))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(162,plain,
% 0.77/0.74 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(f3(c4), f4(c4))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.77/0.74 tff(163,plain,
% 0.77/0.74 (big_r(f3(c4), f4(c4))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[162, 90, 5, 4, 1])).
% 0.77/0.74 tff(164,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(c2, f1(c2)) | big_p(f4(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(c2, f1(c2)) | big_p(f4(c2)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(165,plain,
% 0.77/0.74 ((big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(c2, f1(c2))) <=> (big_p(c2) | big_r(c2, f1(c2)) | big_p(f4(c2)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(166,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(c2, f1(c2)) | big_p(f4(c2))))),
% 0.77/0.74 inference(monotonicity,[status(thm)],[165])).
% 0.77/0.74 tff(167,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(c2, f1(c2)) | big_p(f4(c2)))),
% 0.77/0.74 inference(transitivity,[status(thm)],[166, 164])).
% 0.77/0.74 tff(168,plain,
% 0.77/0.74 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(c2, f1(c2)))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(169,plain,
% 0.77/0.74 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(c2, f1(c2)) | big_p(f4(c2))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.77/0.74 tff(170,plain,
% 0.77/0.74 (big_p(f4(c2))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[169, 48, 4, 1])).
% 0.77/0.74 tff(171,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(172,plain,
% 0.77/0.74 ((big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2))) <=> (big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(173,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2))))),
% 0.77/0.74 inference(monotonicity,[status(thm)],[172])).
% 0.77/0.74 tff(174,plain,
% 0.77/0.74 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2)))),
% 0.77/0.75 inference(transitivity,[status(thm)],[173, 171])).
% 0.77/0.75 tff(175,plain,
% 0.77/0.75 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2)))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(176,plain,
% 0.77/0.75 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.77/0.75 tff(177,plain,
% 0.77/0.75 (big_r(c2, f3(c2)) | big_r(c2, f1(c2))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[176, 69, 4])).
% 0.77/0.75 tff(178,plain,
% 0.77/0.75 (big_r(c2, f3(c2))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[177, 1])).
% 0.77/0.75 tff(179,plain,
% 0.77/0.75 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(180,plain,
% 0.77/0.75 ((big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2))) <=> (big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(181,plain,
% 0.77/0.75 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2))))),
% 0.77/0.75 inference(monotonicity,[status(thm)],[180])).
% 0.77/0.75 tff(182,plain,
% 0.77/0.75 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2)))),
% 0.77/0.75 inference(transitivity,[status(thm)],[181, 179])).
% 0.77/0.75 tff(183,plain,
% 0.77/0.75 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2)))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(184,plain,
% 0.77/0.75 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.77/0.75 tff(185,plain,
% 0.77/0.75 (big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[184, 90, 4])).
% 0.77/0.75 tff(186,plain,
% 0.77/0.75 (big_r(f3(c2), f4(c2))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[185, 1])).
% 0.77/0.75 tff(187,plain,
% 0.77/0.75 (^[X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : refl(((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) <=> ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))))),
% 0.77/0.75 inference(bind,[status(th)],[])).
% 0.77/0.75 tff(188,plain,
% 0.77/0.75 (![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) <=> ![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))),
% 0.77/0.75 inference(quant_intro,[status(thm)],[187])).
% 0.77/0.75 tff(189,plain,
% 0.77/0.75 (![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) <=> ![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(190,plain,
% 0.77/0.75 (^[X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) <=> ((~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9)))), (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) <=> (((~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_p(X3))))), rewrite((((~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_p(X3))) <=> ((~big_p(X3)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9)))), (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) <=> ((~big_p(X3)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))))), ((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) <=> (((~big_p(X3)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(c4, X4))))), rewrite((((~big_p(X3)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(c4, X4))) <=> ((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9)))), ((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) <=> ((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))))), (((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> (((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(X4, X3))))), rewrite((((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(X4, X3))) <=> ((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))), (((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> ((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))))), ((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) <=> (((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_p(X5))))), rewrite((((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_p(X5))) <=> ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))), ((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) <=> ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))))), (((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) <=> (((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(c4, X6))))), rewrite((((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(c4, X6))) <=> ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))), (((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) <=> ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))))), ((((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> (((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(X6, X5))))), rewrite((((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(X6, X5))) <=> ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))), ((((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))))),
% 0.77/0.75 inference(bind,[status(th)],[])).
% 0.77/0.75 tff(191,plain,
% 0.77/0.75 (![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : (((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> ![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))),
% 0.77/0.75 inference(quant_intro,[status(thm)],[190])).
% 0.77/0.75 tff(192,axiom,(![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : (((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_84')).
% 0.77/0.75 tff(193,plain,
% 0.77/0.75 (![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.77/0.75 tff(194,plain,
% 0.77/0.75 (![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.77/0.75 tff(195,plain,(
% 0.77/0.75 ![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))),
% 0.77/0.75 inference(skolemize,[status(sab)],[194])).
% 0.77/0.75 tff(196,plain,
% 0.77/0.75 (![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[195, 188])).
% 0.77/0.75 tff(197,plain,
% 0.77/0.75 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(198,plain,
% 0.77/0.75 (((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2)))) <=> ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(199,plain,
% 0.77/0.75 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4)))))),
% 0.77/0.75 inference(monotonicity,[status(thm)],[198])).
% 0.77/0.75 tff(200,plain,
% 0.77/0.75 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.77/0.75 inference(transitivity,[status(thm)],[199, 197])).
% 0.77/0.75 tff(201,plain,
% 0.77/0.75 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(202,plain,
% 0.77/0.75 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4)))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.77/0.75 tff(203,plain,
% 0.77/0.75 (~big_p(f4(c4))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[202, 196, 186, 178, 170, 163, 156])).
% 0.77/0.75 tff(204,plain,
% 0.77/0.75 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_p(f4(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_p(f4(c4)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(205,plain,
% 0.77/0.75 ((big_p(f4(c4)) | big_p(c4) | big_p(c2) | big_r(c2, f1(c2))) <=> (big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_p(f4(c4)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(206,plain,
% 0.77/0.75 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(f4(c4)) | big_p(c4) | big_p(c2) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_p(f4(c4))))),
% 0.77/0.75 inference(monotonicity,[status(thm)],[205])).
% 0.77/0.75 tff(207,plain,
% 0.77/0.75 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(f4(c4)) | big_p(c4) | big_p(c2) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_p(f4(c4)))),
% 0.77/0.75 inference(transitivity,[status(thm)],[206, 204])).
% 0.77/0.75 tff(208,plain,
% 0.77/0.75 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(f4(c4)) | big_p(c4) | big_p(c2) | big_r(c2, f1(c2)))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(209,plain,
% 0.77/0.75 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_p(f4(c4))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.77/0.75 tff(210,plain,
% 0.77/0.75 ($false),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[209, 48, 5, 4, 1, 203])).
% 0.77/0.75 tff(211,plain,(big_r(c2, f1(c2)) | big_p(c4) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.75 tff(212,plain,
% 0.77/0.75 (big_r(c2, f1(c2))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[211, 5, 4])).
% 0.77/0.75 tff(213,plain,
% 0.77/0.75 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f1(c2), f2(c2)) | big_r(c2, f3(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_r(c2, f3(c2)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(214,plain,
% 0.77/0.75 ((big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(f1(c2), f2(c2))) <=> (big_p(c2) | big_r(f1(c2), f2(c2)) | big_r(c2, f3(c2)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(215,plain,
% 0.77/0.75 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f1(c2), f2(c2)) | big_r(c2, f3(c2))))),
% 0.77/0.75 inference(monotonicity,[status(thm)],[214])).
% 0.77/0.75 tff(216,plain,
% 0.77/0.75 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_r(c2, f3(c2)))),
% 0.77/0.75 inference(transitivity,[status(thm)],[215, 213])).
% 0.77/0.75 tff(217,plain,
% 0.77/0.75 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(f1(c2), f2(c2)))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(218,plain,
% 0.77/0.75 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_r(c2, f3(c2))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.77/0.75 tff(219,plain,
% 0.77/0.75 (big_r(f1(c2), f2(c2)) | big_r(c2, f3(c2))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[218, 144, 4])).
% 0.77/0.75 tff(220,plain,
% 0.77/0.75 (big_r(f1(c2), f2(c2))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[219, 99])).
% 0.77/0.75 tff(221,plain,
% 0.77/0.75 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f1(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f1(c2))))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(222,plain,
% 0.77/0.75 (((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f1(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c2)))) <=> ((~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f1(c2))))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(223,plain,
% 0.77/0.75 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f1(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f1(c2)))))),
% 0.77/0.76 inference(monotonicity,[status(thm)],[222])).
% 0.77/0.76 tff(224,plain,
% 0.77/0.76 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f1(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f1(c2))))),
% 0.77/0.76 inference(transitivity,[status(thm)],[223, 221])).
% 0.77/0.76 tff(225,plain,
% 0.77/0.76 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f1(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c2))))),
% 0.77/0.76 inference(quant_inst,[status(thm)],[])).
% 0.77/0.76 tff(226,plain,
% 0.77/0.76 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f1(c2)))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.77/0.76 tff(227,plain,
% 0.77/0.76 ((~big_p(f2(c2))) | (~big_p(f2(c4)))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[226, 196, 220, 212, 149, 131])).
% 0.77/0.76 tff(228,plain,
% 0.77/0.76 ($false),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[227, 126, 119])).
% 0.77/0.76 tff(229,plain,(big_r(c2, f3(c2)) | big_p(c4) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.76 tff(230,plain,
% 0.77/0.76 (big_r(c2, f3(c2))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[229, 5, 4])).
% 0.77/0.76 tff(231,assumption,(~big_r(f3(c2), f4(c2))), introduced(assumption)).
% 0.77/0.76 tff(232,plain,
% 0.77/0.76 (^[X7: $i, X1: $i] : refl((big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1))) <=> (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1))))),
% 0.77/0.76 inference(bind,[status(th)],[])).
% 0.77/0.76 tff(233,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.77/0.76 inference(quant_intro,[status(thm)],[232])).
% 0.77/0.76 tff(234,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(235,plain,
% 0.77/0.76 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1))) <=> ($false | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1))))), rewrite(($false | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1))) <=> (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))), (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1))) <=> (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))))),
% 0.77/0.76 inference(bind,[status(th)],[])).
% 0.77/0.76 tff(236,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.77/0.76 inference(quant_intro,[status(thm)],[235])).
% 0.77/0.76 tff(237,plain,
% 0.77/0.76 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_p(f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) | big_r(f3(X1), f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))))),
% 0.77/0.76 inference(bind,[status(th)],[])).
% 0.77/0.76 tff(238,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.77/0.76 inference(quant_intro,[status(thm)],[237])).
% 0.77/0.76 tff(239,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.77/0.76 tff(240,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.77/0.76 tff(241,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[240, 236])).
% 0.77/0.76 tff(242,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[241, 234])).
% 0.77/0.76 tff(243,plain,(
% 0.77/0.76 ![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.77/0.76 inference(skolemize,[status(sab)],[242])).
% 0.77/0.76 tff(244,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[243, 233])).
% 0.77/0.76 tff(245,plain,
% 0.77/0.76 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(246,plain,
% 0.77/0.76 ((big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c2), f4(c2))) <=> (big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(247,plain,
% 0.77/0.76 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c2), f4(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_p(f2(c4))))),
% 0.77/0.76 inference(monotonicity,[status(thm)],[246])).
% 0.77/0.76 tff(248,plain,
% 0.77/0.76 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c2), f4(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)))),
% 0.77/0.76 inference(transitivity,[status(thm)],[247, 245])).
% 0.77/0.76 tff(249,plain,
% 0.77/0.76 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c2), f4(c2)))),
% 0.77/0.76 inference(quant_inst,[status(thm)],[])).
% 0.77/0.76 tff(250,plain,
% 0.77/0.76 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_p(f2(c4))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.77/0.76 tff(251,plain,
% 0.77/0.76 (big_r(f3(c2), f4(c2)) | big_p(f2(c4))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[250, 244, 5, 4])).
% 0.77/0.76 tff(252,plain,
% 0.77/0.76 (big_p(f2(c4))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[251, 231])).
% 0.77/0.76 tff(253,plain,
% 0.77/0.76 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(c4, f1(c4)))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(254,plain,
% 0.77/0.76 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(c4, f1(c4)))),
% 0.77/0.76 inference(quant_inst,[status(thm)],[])).
% 0.77/0.76 tff(255,plain,
% 0.77/0.76 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(c4, f1(c4))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.77/0.76 tff(256,plain,
% 0.77/0.76 (big_r(f3(c2), f4(c2)) | big_r(c4, f1(c4))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[255, 90, 5, 4])).
% 0.77/0.76 tff(257,plain,
% 0.77/0.76 (big_r(c4, f1(c4))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[256, 231])).
% 0.77/0.76 tff(258,assumption,(~big_r(f1(c4), f2(c4))), introduced(assumption)).
% 0.77/0.76 tff(259,plain,
% 0.77/0.76 (^[X7: $i, X1: $i] : refl((big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) <=> (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))))),
% 0.77/0.76 inference(bind,[status(th)],[])).
% 0.77/0.76 tff(260,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.77/0.76 inference(quant_intro,[status(thm)],[259])).
% 0.77/0.76 tff(261,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(262,plain,
% 0.77/0.76 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) <=> ($false | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))))), rewrite(($false | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) <=> (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) <=> (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))))),
% 0.77/0.76 inference(bind,[status(th)],[])).
% 0.77/0.76 tff(263,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.77/0.76 inference(quant_intro,[status(thm)],[262])).
% 0.77/0.76 tff(264,plain,
% 0.77/0.76 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))))),
% 0.77/0.76 inference(bind,[status(th)],[])).
% 0.77/0.76 tff(265,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.77/0.76 inference(quant_intro,[status(thm)],[264])).
% 0.77/0.76 tff(266,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_13')).
% 0.77/0.76 tff(267,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.77/0.76 tff(268,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[267, 263])).
% 0.77/0.76 tff(269,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[268, 261])).
% 0.77/0.76 tff(270,plain,(
% 0.77/0.76 ![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.77/0.76 inference(skolemize,[status(sab)],[269])).
% 0.77/0.76 tff(271,plain,
% 0.77/0.76 (![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[270, 260])).
% 0.77/0.76 tff(272,plain,
% 0.77/0.76 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(f1(c4), f2(c4)) | big_p(f4(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f1(c4), f2(c4)) | big_p(f4(c4)))),
% 0.80/0.76 inference(rewrite,[status(thm)],[])).
% 0.80/0.76 tff(273,plain,
% 0.80/0.76 ((big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(f1(c4), f2(c4))) <=> (big_p(c4) | big_r(f1(c4), f2(c4)) | big_p(f4(c4)))),
% 0.80/0.76 inference(rewrite,[status(thm)],[])).
% 0.80/0.76 tff(274,plain,
% 0.80/0.76 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(f1(c4), f2(c4)) | big_p(f4(c4))))),
% 0.80/0.76 inference(monotonicity,[status(thm)],[273])).
% 0.80/0.76 tff(275,plain,
% 0.80/0.76 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f1(c4), f2(c4)) | big_p(f4(c4)))),
% 0.80/0.76 inference(transitivity,[status(thm)],[274, 272])).
% 0.80/0.76 tff(276,plain,
% 0.80/0.76 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(f1(c4), f2(c4)))),
% 0.80/0.76 inference(quant_inst,[status(thm)],[])).
% 0.80/0.76 tff(277,plain,
% 0.80/0.76 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f1(c4), f2(c4)) | big_p(f4(c4))),
% 0.80/0.76 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.80/0.76 tff(278,plain,
% 0.80/0.76 (big_p(f4(c4))),
% 0.80/0.76 inference(unit_resolution,[status(thm)],[277, 271, 5, 258])).
% 0.80/0.76 tff(279,plain,
% 0.80/0.76 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.76 inference(rewrite,[status(thm)],[])).
% 0.80/0.76 tff(280,plain,
% 0.80/0.76 ((big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(f1(c4), f2(c4))) <=> (big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.76 inference(rewrite,[status(thm)],[])).
% 0.80/0.76 tff(281,plain,
% 0.80/0.76 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(f1(c4), f2(c4))))),
% 0.80/0.76 inference(monotonicity,[status(thm)],[280])).
% 0.80/0.76 tff(282,plain,
% 0.80/0.76 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.76 inference(transitivity,[status(thm)],[281, 279])).
% 0.80/0.76 tff(283,plain,
% 0.80/0.76 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(f1(c4), f2(c4)))),
% 0.80/0.76 inference(quant_inst,[status(thm)],[])).
% 0.80/0.76 tff(284,plain,
% 0.80/0.76 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(f1(c4), f2(c4))),
% 0.80/0.76 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.80/0.76 tff(285,plain,
% 0.80/0.76 (big_p(f4(c2))),
% 0.80/0.76 inference(unit_resolution,[status(thm)],[284, 271, 5, 4, 258])).
% 0.80/0.76 tff(286,plain,
% 0.80/0.76 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.76 inference(rewrite,[status(thm)],[])).
% 0.80/0.76 tff(287,plain,
% 0.80/0.76 ((big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4))) <=> (big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(288,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4))))),
% 0.80/0.77 inference(monotonicity,[status(thm)],[287])).
% 0.80/0.77 tff(289,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.77 inference(transitivity,[status(thm)],[288, 286])).
% 0.80/0.77 tff(290,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.77 inference(quant_inst,[status(thm)],[])).
% 0.80/0.77 tff(291,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.80/0.77 tff(292,plain,
% 0.80/0.77 (big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[291, 144, 5])).
% 0.80/0.77 tff(293,plain,
% 0.80/0.77 (big_r(c4, f3(c4))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[292, 258])).
% 0.80/0.77 tff(294,plain,
% 0.80/0.77 (^[X7: $i, X1: $i] : refl((big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7))) <=> (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7))))),
% 0.80/0.77 inference(bind,[status(th)],[])).
% 0.80/0.77 tff(295,plain,
% 0.80/0.77 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.77 inference(quant_intro,[status(thm)],[294])).
% 0.80/0.77 tff(296,plain,
% 0.80/0.77 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(297,plain,
% 0.80/0.77 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7))) <=> ($false | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7))))), rewrite(($false | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7))) <=> (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))), (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7))) <=> (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))))),
% 0.80/0.77 inference(bind,[status(th)],[])).
% 0.80/0.77 tff(298,plain,
% 0.80/0.77 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.77 inference(quant_intro,[status(thm)],[297])).
% 0.80/0.77 tff(299,plain,
% 0.80/0.77 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_r(f3(X1), f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))))),
% 0.80/0.77 inference(bind,[status(th)],[])).
% 0.80/0.77 tff(300,plain,
% 0.80/0.77 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.77 inference(quant_intro,[status(thm)],[299])).
% 0.80/0.77 tff(301,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_15')).
% 0.80/0.77 tff(302,plain,
% 0.80/0.77 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.80/0.77 tff(303,plain,
% 0.80/0.77 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.80/0.77 tff(304,plain,
% 0.80/0.77 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[303, 296])).
% 0.80/0.77 tff(305,plain,(
% 0.80/0.77 ![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.77 inference(skolemize,[status(sab)],[304])).
% 0.80/0.77 tff(306,plain,
% 0.80/0.77 (![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[305, 295])).
% 0.80/0.77 tff(307,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(308,plain,
% 0.80/0.77 ((big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4))) <=> (big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(309,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4))))),
% 0.80/0.77 inference(monotonicity,[status(thm)],[308])).
% 0.80/0.77 tff(310,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.77 inference(transitivity,[status(thm)],[309, 307])).
% 0.80/0.77 tff(311,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.77 inference(quant_inst,[status(thm)],[])).
% 0.80/0.77 tff(312,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.80/0.77 tff(313,plain,
% 0.80/0.77 (big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[312, 306, 5])).
% 0.80/0.77 tff(314,plain,
% 0.80/0.77 (big_r(f3(c4), f4(c4))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[313, 258])).
% 0.80/0.77 tff(315,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(316,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.77 inference(quant_inst,[status(thm)],[])).
% 0.80/0.77 tff(317,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(f1(c4), f2(c4))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.80/0.77 tff(318,plain,
% 0.80/0.77 (big_r(f3(c2), f4(c2)) | big_r(f1(c4), f2(c4))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[317, 306, 5, 4])).
% 0.80/0.77 tff(319,plain,
% 0.80/0.77 (big_r(f3(c2), f4(c2))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[318, 258])).
% 0.80/0.77 tff(320,plain,
% 0.80/0.77 ((~big_p(f4(c2))) | (~big_p(f4(c4)))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[202, 196, 319, 230, 314, 293])).
% 0.80/0.77 tff(321,plain,
% 0.80/0.77 ($false),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[320, 285, 278])).
% 0.80/0.77 tff(322,plain,(big_r(f1(c4), f2(c4)) | big_p(c4) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.77 tff(323,plain,
% 0.80/0.77 (big_r(f1(c4), f2(c4))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[322, 5, 4])).
% 0.80/0.77 tff(324,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(325,plain,
% 0.80/0.77 ((big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2))) <=> (big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(326,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2))))),
% 0.80/0.77 inference(monotonicity,[status(thm)],[325])).
% 0.80/0.77 tff(327,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2)))),
% 0.80/0.77 inference(transitivity,[status(thm)],[326, 324])).
% 0.80/0.77 tff(328,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2)))),
% 0.80/0.77 inference(quant_inst,[status(thm)],[])).
% 0.80/0.77 tff(329,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.80/0.77 tff(330,plain,
% 0.80/0.77 (big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[329, 306, 4])).
% 0.80/0.77 tff(331,plain,
% 0.80/0.77 (big_r(f1(c2), f2(c2))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[330, 231])).
% 0.80/0.77 tff(332,plain,
% 0.80/0.77 (~big_p(f2(c2))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[226, 196, 331, 212, 323, 257, 252])).
% 0.80/0.77 tff(333,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c2)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(334,plain,
% 0.80/0.77 ((big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(f3(c2), f4(c2))) <=> (big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c2)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(335,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(f3(c2), f4(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c2))))),
% 0.80/0.77 inference(monotonicity,[status(thm)],[334])).
% 0.80/0.77 tff(336,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(f3(c2), f4(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c2)))),
% 0.80/0.77 inference(transitivity,[status(thm)],[335, 333])).
% 0.80/0.77 tff(337,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(f3(c2), f4(c2)))),
% 0.80/0.77 inference(quant_inst,[status(thm)],[])).
% 0.80/0.77 tff(338,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c2))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.80/0.77 tff(339,plain,
% 0.80/0.77 ($false),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[338, 244, 4, 231, 332])).
% 0.80/0.77 tff(340,plain,(big_r(f3(c2), f4(c2)) | big_p(c2) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.77 tff(341,plain,
% 0.80/0.77 (big_r(f3(c2), f4(c2))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[340, 5, 4])).
% 0.80/0.77 tff(342,plain,
% 0.80/0.77 (~big_p(f4(c4))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[202, 196, 341, 230, 98, 77, 56])).
% 0.80/0.77 tff(343,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(c4, f1(c4)) | big_p(f4(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c4, f1(c4)) | big_p(f4(c4)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(344,plain,
% 0.80/0.77 ((big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(c4, f1(c4))) <=> (big_p(c4) | big_r(c4, f1(c4)) | big_p(f4(c4)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(345,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(c4, f1(c4)) | big_p(f4(c4))))),
% 0.80/0.77 inference(monotonicity,[status(thm)],[344])).
% 0.80/0.77 tff(346,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c4, f1(c4)) | big_p(f4(c4)))),
% 0.80/0.77 inference(transitivity,[status(thm)],[345, 343])).
% 0.80/0.77 tff(347,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(c4, f1(c4)))),
% 0.80/0.77 inference(quant_inst,[status(thm)],[])).
% 0.80/0.77 tff(348,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c4, f1(c4)) | big_p(f4(c4))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.80/0.77 tff(349,plain,
% 0.80/0.77 ($false),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[348, 48, 5, 3, 342])).
% 0.80/0.77 tff(350,plain,(big_r(c4, f1(c4)) | big_p(c4) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.77 tff(351,plain,
% 0.80/0.77 (big_r(c4, f1(c4))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[350, 5, 4])).
% 0.80/0.77 tff(352,assumption,(~big_r(f1(c2), f2(c2))), introduced(assumption)).
% 0.80/0.77 tff(353,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f1(c2), f2(c2)) | big_p(f4(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_p(f4(c2)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(354,plain,
% 0.80/0.77 ((big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(f1(c2), f2(c2))) <=> (big_p(c2) | big_r(f1(c2), f2(c2)) | big_p(f4(c2)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(355,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f1(c2), f2(c2)) | big_p(f4(c2))))),
% 0.80/0.77 inference(monotonicity,[status(thm)],[354])).
% 0.80/0.77 tff(356,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_p(f4(c2)))),
% 0.80/0.77 inference(transitivity,[status(thm)],[355, 353])).
% 0.80/0.77 tff(357,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(f1(c2), f2(c2)))),
% 0.80/0.77 inference(quant_inst,[status(thm)],[])).
% 0.80/0.77 tff(358,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_p(f4(c2))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.80/0.77 tff(359,plain,
% 0.80/0.77 (big_r(f1(c2), f2(c2)) | big_p(f4(c2))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[358, 271, 4])).
% 0.80/0.77 tff(360,plain,
% 0.80/0.77 (big_p(f4(c2))),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[359, 352])).
% 0.80/0.77 tff(361,assumption,(~big_r(c4, f3(c4))), introduced(assumption)).
% 0.80/0.77 tff(362,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c4)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(363,plain,
% 0.80/0.77 ((big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(c4, f3(c4))) <=> (big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c4)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(364,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(c4, f3(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c4))))),
% 0.80/0.77 inference(monotonicity,[status(thm)],[363])).
% 0.80/0.77 tff(365,plain,
% 0.80/0.77 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(c4, f3(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c4)))),
% 0.80/0.77 inference(transitivity,[status(thm)],[364, 362])).
% 0.80/0.77 tff(366,plain,
% 0.80/0.77 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(c4, f3(c4)))),
% 0.80/0.77 inference(quant_inst,[status(thm)],[])).
% 0.80/0.78 tff(367,plain,
% 0.80/0.78 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c4))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.80/0.78 tff(368,plain,
% 0.80/0.78 (big_r(c4, f3(c4)) | big_p(f2(c4))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[367, 112, 5])).
% 0.80/0.78 tff(369,plain,
% 0.80/0.78 (big_p(f2(c4))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[368, 361])).
% 0.80/0.78 tff(370,plain,
% 0.80/0.78 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(371,plain,
% 0.80/0.78 (((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2)))) <=> ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(372,plain,
% 0.80/0.78 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4)))))),
% 0.80/0.78 inference(monotonicity,[status(thm)],[371])).
% 0.80/0.78 tff(373,plain,
% 0.80/0.78 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.80/0.78 inference(transitivity,[status(thm)],[372, 370])).
% 0.80/0.78 tff(374,plain,
% 0.80/0.78 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))),
% 0.80/0.78 inference(quant_inst,[status(thm)],[])).
% 0.80/0.78 tff(375,plain,
% 0.80/0.78 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4)))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.80/0.78 tff(376,plain,
% 0.80/0.78 ((~big_p(f4(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4)))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[375, 196, 341, 230, 323])).
% 0.80/0.78 tff(377,plain,
% 0.80/0.78 (~big_p(f4(c2))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[376, 369, 351])).
% 0.80/0.78 tff(378,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(c4, f3(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(c4, f3(c4)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(379,plain,
% 0.80/0.78 ((big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(f1(c2), f2(c2))) <=> (big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(c4, f3(c4)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(380,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(c4, f3(c4))))),
% 0.80/0.78 inference(monotonicity,[status(thm)],[379])).
% 0.80/0.78 tff(381,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(c4, f3(c4)))),
% 0.80/0.78 inference(transitivity,[status(thm)],[380, 378])).
% 0.80/0.78 tff(382,plain,
% 0.80/0.78 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(f1(c2), f2(c2)))),
% 0.80/0.78 inference(quant_inst,[status(thm)],[])).
% 0.80/0.78 tff(383,plain,
% 0.80/0.78 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(c4, f3(c4))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.80/0.78 tff(384,plain,
% 0.80/0.78 (big_r(f1(c2), f2(c2)) | big_r(c4, f3(c4))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[383, 144, 5, 4])).
% 0.80/0.78 tff(385,plain,
% 0.80/0.78 (big_r(f1(c2), f2(c2))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[384, 361])).
% 0.80/0.78 tff(386,plain,
% 0.80/0.78 (~big_p(f2(c2))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[226, 196, 385, 212, 323, 351, 369])).
% 0.80/0.78 tff(387,plain,
% 0.80/0.78 ($false),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[33, 19, 4, 386, 377])).
% 0.80/0.78 tff(388,plain,(big_r(c4, f3(c4)) | big_p(c2) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.78 tff(389,plain,
% 0.80/0.78 (big_r(c4, f3(c4))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[388, 5, 4])).
% 0.80/0.78 tff(390,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(f3(c4), f4(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(f3(c4), f4(c4)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(391,plain,
% 0.80/0.78 ((big_p(c4) | big_p(c2) | big_r(f3(c4), f4(c4)) | big_r(f1(c2), f2(c2))) <=> (big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(f3(c4), f4(c4)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(392,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(c2) | big_r(f3(c4), f4(c4)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(f3(c4), f4(c4))))),
% 0.80/0.78 inference(monotonicity,[status(thm)],[391])).
% 0.80/0.78 tff(393,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(c2) | big_r(f3(c4), f4(c4)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(f3(c4), f4(c4)))),
% 0.80/0.78 inference(transitivity,[status(thm)],[392, 390])).
% 0.80/0.78 tff(394,plain,
% 0.80/0.78 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(c2) | big_r(f3(c4), f4(c4)) | big_r(f1(c2), f2(c2)))),
% 0.80/0.78 inference(quant_inst,[status(thm)],[])).
% 0.80/0.78 tff(395,plain,
% 0.80/0.78 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(f3(c4), f4(c4))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.80/0.78 tff(396,plain,
% 0.80/0.78 (big_r(f1(c2), f2(c2)) | big_r(f3(c4), f4(c4))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[395, 306, 5, 4])).
% 0.80/0.78 tff(397,plain,
% 0.80/0.78 (big_r(f3(c4), f4(c4))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[396, 352])).
% 0.80/0.78 tff(398,plain,
% 0.80/0.78 (~big_p(f4(c4))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[202, 196, 341, 230, 397, 389, 360])).
% 0.80/0.78 tff(399,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_p(f4(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_p(f4(c4)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(400,plain,
% 0.80/0.78 ((big_p(f4(c4)) | big_p(c4) | big_p(c2) | big_r(f1(c2), f2(c2))) <=> (big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_p(f4(c4)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(401,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c4)) | big_p(c4) | big_p(c2) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_p(f4(c4))))),
% 0.80/0.78 inference(monotonicity,[status(thm)],[400])).
% 0.80/0.78 tff(402,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c4)) | big_p(c4) | big_p(c2) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_p(f4(c4)))),
% 0.80/0.78 inference(transitivity,[status(thm)],[401, 399])).
% 0.80/0.78 tff(403,plain,
% 0.80/0.78 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c4)) | big_p(c4) | big_p(c2) | big_r(f1(c2), f2(c2)))),
% 0.80/0.78 inference(quant_inst,[status(thm)],[])).
% 0.80/0.78 tff(404,plain,
% 0.80/0.78 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_p(f4(c4))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[403, 402])).
% 0.80/0.78 tff(405,plain,
% 0.80/0.78 ($false),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[404, 271, 5, 4, 352, 398])).
% 0.80/0.78 tff(406,plain,(big_r(f1(c2), f2(c2)) | big_p(c4) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.78 tff(407,plain,
% 0.80/0.78 (big_r(f1(c2), f2(c2))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[406, 5, 4])).
% 0.80/0.78 tff(408,plain,
% 0.80/0.78 ((~big_p(f2(c2))) | (~big_p(f2(c4)))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[226, 196, 407, 212, 323, 351])).
% 0.80/0.78 tff(409,plain,
% 0.80/0.78 ($false),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[408, 35, 27])).
% 0.80/0.78 tff(410,plain,(big_p(f4(c2)) | big_p(c2) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.78 tff(411,plain,
% 0.80/0.78 (big_p(f4(c2))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[410, 5, 4])).
% 0.80/0.78 tff(412,plain,
% 0.80/0.78 (~big_p(f2(c4))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[376, 411, 351])).
% 0.80/0.78 tff(413,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c4)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(414,plain,
% 0.80/0.78 ((big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c4), f4(c4))) <=> (big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c4)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(415,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c4), f4(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c4))))),
% 0.80/0.78 inference(monotonicity,[status(thm)],[414])).
% 0.80/0.78 tff(416,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c4), f4(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c4)))),
% 0.80/0.78 inference(transitivity,[status(thm)],[415, 413])).
% 0.80/0.78 tff(417,plain,
% 0.80/0.78 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c4), f4(c4)))),
% 0.80/0.78 inference(quant_inst,[status(thm)],[])).
% 0.80/0.78 tff(418,plain,
% 0.80/0.78 ((~![X7: $i, X1: $i] : (big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c4))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.80/0.78 tff(419,plain,
% 0.80/0.78 (big_r(f3(c4), f4(c4)) | big_p(f2(c4))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[418, 244, 5])).
% 0.80/0.78 tff(420,plain,
% 0.80/0.78 (big_r(f3(c4), f4(c4))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[419, 412])).
% 0.80/0.78 tff(421,plain,
% 0.80/0.78 (~big_p(f4(c4))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[202, 196, 341, 230, 420, 389, 411])).
% 0.80/0.78 tff(422,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(c4) | big_p(f4(c4)) | big_p(f2(c4)))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | big_p(c4) | big_p(f4(c4)) | big_p(f2(c4)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(423,plain,
% 0.80/0.78 ((big_p(f4(c4)) | big_p(c4) | big_p(f2(c4)) | big_p(c4)) <=> (big_p(c4) | big_p(f4(c4)) | big_p(f2(c4)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(424,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(f4(c4)) | big_p(c4) | big_p(f2(c4)) | big_p(c4))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(c4) | big_p(f4(c4)) | big_p(f2(c4))))),
% 0.80/0.78 inference(monotonicity,[status(thm)],[423])).
% 0.80/0.78 tff(425,plain,
% 0.80/0.78 (((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(f4(c4)) | big_p(c4) | big_p(f2(c4)) | big_p(c4))) <=> ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | big_p(c4) | big_p(f4(c4)) | big_p(f2(c4)))),
% 0.80/0.78 inference(transitivity,[status(thm)],[424, 422])).
% 0.80/0.78 tff(426,plain,
% 0.80/0.78 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (big_p(f4(c4)) | big_p(c4) | big_p(f2(c4)) | big_p(c4))),
% 0.80/0.78 inference(quant_inst,[status(thm)],[])).
% 0.80/0.78 tff(427,plain,
% 0.80/0.78 ((~![X7: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | big_p(c4) | big_p(f4(c4)) | big_p(f2(c4))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.80/0.78 tff(428,plain,
% 0.80/0.78 ($false),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[427, 19, 5, 412, 421])).
% 0.80/0.78 tff(429,plain,(big_p(c4) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.78 tff(430,plain,
% 0.80/0.78 (big_p(c4)),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[429, 4])).
% 0.80/0.78 tff(431,assumption,(~big_r(c4, c3)), introduced(assumption)).
% 0.80/0.78 tff(432,plain,
% 0.80/0.78 (big_r(c2, f1(c2))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[177, 99])).
% 0.80/0.78 tff(433,plain,
% 0.80/0.78 (^[X9: $i, X10: $i] : refl(((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10))) <=> ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10))))),
% 0.80/0.78 inference(bind,[status(th)],[])).
% 0.80/0.78 tff(434,plain,
% 0.80/0.78 (![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10))) <=> ![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.80/0.78 inference(quant_intro,[status(thm)],[433])).
% 0.80/0.78 tff(435,plain,
% 0.80/0.78 (![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10))) <=> ![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(436,plain,
% 0.80/0.78 (^[X9: $i, X10: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) <=> ((~big_p(X9)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))), (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) <=> (((~big_p(X9)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | (~big_p(c4))))), rewrite((((~big_p(X9)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | (~big_p(c4))) <=> ((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))), (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) <=> ((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))))), ((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_r(c4, c3)) <=> (((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | big_r(c4, c3)))), rewrite((((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | big_r(c4, c3)) <=> ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))), ((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_r(c4, c3)) <=> ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))))),
% 0.80/0.78 inference(bind,[status(th)],[])).
% 0.80/0.78 tff(437,plain,
% 0.80/0.78 (![X9: $i, X10: $i] : (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_r(c4, c3)) <=> ![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.80/0.78 inference(quant_intro,[status(thm)],[436])).
% 0.80/0.78 tff(438,axiom,(![X9: $i, X10: $i] : (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_r(c4, c3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_79')).
% 0.80/0.78 tff(439,plain,
% 0.80/0.78 (![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.80/0.78 tff(440,plain,
% 0.80/0.78 (![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[439, 435])).
% 0.80/0.78 tff(441,plain,(
% 0.80/0.78 ![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.80/0.78 inference(skolemize,[status(sab)],[440])).
% 0.80/0.78 tff(442,plain,
% 0.80/0.78 (![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[441, 434])).
% 0.80/0.78 tff(443,plain,
% 0.80/0.78 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(444,plain,
% 0.80/0.78 (((~big_p(f2(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2)))) <=> ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(445,plain,
% 0.80/0.78 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f2(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2)))))),
% 0.80/0.79 inference(monotonicity,[status(thm)],[444])).
% 0.80/0.79 tff(446,plain,
% 0.80/0.79 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f2(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.80/0.79 inference(transitivity,[status(thm)],[445, 443])).
% 0.80/0.79 tff(447,plain,
% 0.80/0.79 ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f2(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.80/0.79 inference(quant_inst,[status(thm)],[])).
% 0.80/0.79 tff(448,plain,
% 0.80/0.79 ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2)))),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.80/0.79 tff(449,plain,
% 0.80/0.79 (~big_p(f2(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[448, 430, 431, 442, 220, 432])).
% 0.80/0.79 tff(450,plain,
% 0.80/0.79 ($false),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[118, 112, 4, 99, 449])).
% 0.80/0.79 tff(451,plain,(big_r(c2, f3(c2)) | big_p(c2) | big_r(c4, c3)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.79 tff(452,plain,
% 0.80/0.79 (big_r(c2, f3(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[451, 4, 431])).
% 0.80/0.79 tff(453,plain,
% 0.80/0.79 (big_r(c2, f1(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[185, 231])).
% 0.80/0.79 tff(454,plain,
% 0.80/0.79 (~big_p(f2(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[448, 430, 431, 442, 331, 453])).
% 0.80/0.79 tff(455,plain,
% 0.80/0.79 ($false),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[338, 244, 4, 231, 454])).
% 0.80/0.79 tff(456,plain,(big_r(f3(c2), f4(c2)) | big_p(c2) | big_r(c4, c3)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.79 tff(457,plain,
% 0.80/0.79 (big_r(f3(c2), f4(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[456, 4, 431])).
% 0.80/0.79 tff(458,plain,
% 0.80/0.79 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(459,plain,
% 0.80/0.79 (((~big_p(f4(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2)))) <=> ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(460,plain,
% 0.80/0.79 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f4(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2)))))),
% 0.80/0.79 inference(monotonicity,[status(thm)],[459])).
% 0.80/0.79 tff(461,plain,
% 0.80/0.79 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f4(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))),
% 0.80/0.79 inference(transitivity,[status(thm)],[460, 458])).
% 0.80/0.79 tff(462,plain,
% 0.80/0.79 ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f4(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2))))),
% 0.80/0.79 inference(quant_inst,[status(thm)],[])).
% 0.80/0.79 tff(463,plain,
% 0.80/0.79 ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2)))),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.80/0.79 tff(464,plain,
% 0.80/0.79 (~big_p(f4(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[463, 430, 431, 442, 457, 452])).
% 0.80/0.79 tff(465,plain,
% 0.80/0.79 (big_r(c2, f1(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[169, 48, 4, 464])).
% 0.80/0.79 tff(466,plain,
% 0.80/0.79 (big_r(f1(c2), f2(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[358, 271, 4, 464])).
% 0.80/0.79 tff(467,plain,
% 0.80/0.79 (~big_p(f2(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[448, 430, 431, 442, 466, 465])).
% 0.80/0.79 tff(468,plain,
% 0.80/0.79 ($false),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[33, 19, 4, 464, 467])).
% 0.80/0.79 tff(469,plain,(big_p(c2) | big_r(c4, c3)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.79 tff(470,plain,
% 0.80/0.79 (big_r(c4, c3)),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[469, 4])).
% 0.80/0.79 tff(471,assumption,(big_p(c4)), introduced(assumption)).
% 0.80/0.79 tff(472,assumption,(~big_p(c3)), introduced(assumption)).
% 0.80/0.79 tff(473,plain,
% 0.80/0.79 (big_r(f3(c2), f4(c2)) | big_p(f2(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[338, 244, 4])).
% 0.80/0.79 tff(474,plain,
% 0.80/0.79 (big_p(f2(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[473, 231])).
% 0.80/0.79 tff(475,plain,
% 0.80/0.79 (big_r(f3(c2), f4(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[330, 352])).
% 0.80/0.79 tff(476,plain,
% 0.80/0.79 (^[X9: $i, X10: $i] : refl((big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) <=> (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))))),
% 0.80/0.79 inference(bind,[status(th)],[])).
% 0.80/0.79 tff(477,plain,
% 0.80/0.79 (![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) <=> ![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.80/0.79 inference(quant_intro,[status(thm)],[476])).
% 0.80/0.79 tff(478,plain,
% 0.80/0.79 (![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) <=> ![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(479,plain,
% 0.80/0.79 (^[X9: $i, X10: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) <=> ((~big_p(X9)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))), (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) <=> (((~big_p(X9)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | (~big_p(c4))))), rewrite((((~big_p(X9)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | (~big_p(c4))) <=> ((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))), (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) <=> ((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))))), ((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_p(c3)) <=> (((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | big_p(c3)))), rewrite((((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | big_p(c3)) <=> (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))), ((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_p(c3)) <=> (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))))),
% 0.80/0.79 inference(bind,[status(th)],[])).
% 0.80/0.79 tff(480,plain,
% 0.80/0.79 (![X9: $i, X10: $i] : (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_p(c3)) <=> ![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.80/0.79 inference(quant_intro,[status(thm)],[479])).
% 0.80/0.79 tff(481,axiom,(![X9: $i, X10: $i] : (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_p(c3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_78')).
% 0.80/0.79 tff(482,plain,
% 0.80/0.79 (![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[481, 480])).
% 0.80/0.79 tff(483,plain,
% 0.80/0.79 (![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[482, 478])).
% 0.80/0.79 tff(484,plain,(
% 0.80/0.79 ![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.80/0.79 inference(skolemize,[status(sab)],[483])).
% 0.80/0.79 tff(485,plain,
% 0.80/0.79 (![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[484, 477])).
% 0.80/0.79 tff(486,plain,
% 0.80/0.79 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(c4)) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(487,plain,
% 0.80/0.79 ((big_p(c3) | (~big_p(f2(c2))) | (~big_p(c4)) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2)))) <=> (big_p(c3) | (~big_p(c4)) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(488,plain,
% 0.80/0.79 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f2(c2))) | (~big_p(c4)) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(c4)) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2)))))),
% 0.80/0.79 inference(monotonicity,[status(thm)],[487])).
% 0.80/0.79 tff(489,plain,
% 0.80/0.79 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f2(c2))) | (~big_p(c4)) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.80/0.79 inference(transitivity,[status(thm)],[488, 486])).
% 0.80/0.79 tff(490,plain,
% 0.80/0.79 ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f2(c2))) | (~big_p(c4)) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.80/0.79 inference(quant_inst,[status(thm)],[])).
% 0.80/0.79 tff(491,plain,
% 0.80/0.79 ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2)))),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.80/0.79 tff(492,plain,
% 0.80/0.79 (~big_p(f2(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[491, 472, 471, 485, 432, 220])).
% 0.80/0.79 tff(493,plain,
% 0.80/0.79 ($false),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[118, 112, 4, 99, 492])).
% 0.80/0.79 tff(494,plain,(big_r(c2, f3(c2)) | big_p(c2) | big_p(c3) | (~big_p(c4))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.79 tff(495,plain,
% 0.80/0.79 (big_r(c2, f3(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[494, 472, 4, 471])).
% 0.80/0.79 tff(496,plain,
% 0.80/0.79 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(c4)) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(497,plain,
% 0.80/0.79 ((big_p(c3) | (~big_p(f4(c2))) | (~big_p(c4)) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2)))) <=> (big_p(c3) | (~big_p(c4)) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(498,plain,
% 0.80/0.79 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f4(c2))) | (~big_p(c4)) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(c4)) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2)))))),
% 0.80/0.79 inference(monotonicity,[status(thm)],[497])).
% 0.80/0.79 tff(499,plain,
% 0.80/0.79 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f4(c2))) | (~big_p(c4)) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))),
% 0.80/0.79 inference(transitivity,[status(thm)],[498, 496])).
% 0.80/0.79 tff(500,plain,
% 0.80/0.79 ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f4(c2))) | (~big_p(c4)) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2))))),
% 0.80/0.79 inference(quant_inst,[status(thm)],[])).
% 0.80/0.79 tff(501,plain,
% 0.80/0.79 ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2)))),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[500, 499])).
% 0.80/0.79 tff(502,plain,
% 0.80/0.79 (~big_p(f4(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[501, 472, 471, 485, 495, 475])).
% 0.80/0.79 tff(503,plain,
% 0.80/0.79 ($false),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[358, 271, 4, 352, 502])).
% 0.80/0.79 tff(504,plain,(big_r(f1(c2), f2(c2)) | big_p(c2) | big_p(c3) | (~big_p(c4))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.79 tff(505,plain,
% 0.80/0.79 (big_r(f1(c2), f2(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[504, 472, 4, 471])).
% 0.80/0.79 tff(506,plain,
% 0.80/0.79 ((~big_p(f2(c2))) | (~big_r(c2, f1(c2)))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[491, 472, 471, 485, 505])).
% 0.80/0.79 tff(507,plain,
% 0.80/0.79 ($false),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[506, 474, 453])).
% 0.80/0.79 tff(508,plain,(big_r(f3(c2), f4(c2)) | big_p(c3) | (~big_p(c4)) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.79 tff(509,plain,
% 0.80/0.79 (big_r(f3(c2), f4(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[508, 472, 471, 4])).
% 0.80/0.79 tff(510,plain,
% 0.80/0.79 (~big_p(f4(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[501, 472, 471, 485, 495, 509])).
% 0.80/0.79 tff(511,plain,
% 0.80/0.79 (big_p(f2(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[33, 19, 4, 510])).
% 0.80/0.79 tff(512,plain,
% 0.80/0.79 (big_r(c2, f1(c2))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[169, 48, 4, 510])).
% 0.80/0.79 tff(513,plain,
% 0.80/0.79 ($false),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[506, 512, 511])).
% 0.80/0.79 tff(514,plain,(big_p(c3) | (~big_p(c4)) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.79 tff(515,plain,
% 0.80/0.79 (big_p(c3)),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[514, 4, 471])).
% 0.80/0.79 tff(516,assumption,(big_r(c4, c3)), introduced(assumption)).
% 0.80/0.79 tff(517,assumption,(big_p(c3)), introduced(assumption)).
% 0.80/0.79 tff(518,plain,
% 0.80/0.79 (^[X7: $i, X8: $i, X1: $i] : refl((big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))),
% 0.80/0.79 inference(bind,[status(th)],[])).
% 0.80/0.79 tff(519,plain,
% 0.80/0.79 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.80/0.79 inference(quant_intro,[status(thm)],[518])).
% 0.80/0.79 tff(520,plain,
% 0.80/0.79 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(521,plain,
% 0.80/0.79 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ($false | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), rewrite(($false | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))))),
% 0.80/0.79 inference(bind,[status(th)],[])).
% 0.80/0.79 tff(522,plain,
% 0.80/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.80/0.79 inference(quant_intro,[status(thm)],[521])).
% 0.80/0.79 tff(523,plain,
% 0.80/0.79 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))))),
% 0.80/0.79 inference(bind,[status(th)],[])).
% 0.80/0.79 tff(524,plain,
% 0.80/0.79 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.80/0.79 inference(quant_intro,[status(thm)],[523])).
% 0.80/0.79 tff(525,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_19')).
% 0.80/0.80 tff(526,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[525, 524])).
% 0.80/0.80 tff(527,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[526, 522])).
% 0.80/0.80 tff(528,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[527, 520])).
% 0.80/0.80 tff(529,plain,(
% 0.80/0.80 ![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.80/0.80 inference(skolemize,[status(sab)],[528])).
% 0.80/0.80 tff(530,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[529, 519])).
% 0.80/0.80 tff(531,plain,
% 0.80/0.80 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(532,plain,
% 0.80/0.80 ((big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> (big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(533,plain,
% 0.80/0.80 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4))))),
% 0.80/0.80 inference(monotonicity,[status(thm)],[532])).
% 0.80/0.80 tff(534,plain,
% 0.80/0.80 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.80/0.80 inference(transitivity,[status(thm)],[533, 531])).
% 0.80/0.80 tff(535,plain,
% 0.80/0.80 ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.80/0.80 inference(quant_inst,[status(thm)],[])).
% 0.80/0.80 tff(536,plain,
% 0.80/0.80 ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[535, 534])).
% 0.80/0.80 tff(537,plain,
% 0.80/0.80 (big_p(f4(c2)) | big_p(f2(c4))),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[536, 530, 517, 4, 516])).
% 0.80/0.80 tff(538,plain,
% 0.80/0.80 (big_p(f2(c4))),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[537, 6])).
% 0.80/0.80 tff(539,plain,
% 0.80/0.80 (^[X7: $i, X8: $i, X1: $i] : refl((big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))),
% 0.80/0.80 inference(bind,[status(th)],[])).
% 0.80/0.80 tff(540,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.80/0.80 inference(quant_intro,[status(thm)],[539])).
% 0.80/0.80 tff(541,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(542,plain,
% 0.80/0.80 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ($false | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), rewrite(($false | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))))),
% 0.80/0.80 inference(bind,[status(th)],[])).
% 0.80/0.80 tff(543,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.80/0.80 inference(quant_intro,[status(thm)],[542])).
% 0.80/0.80 tff(544,plain,
% 0.80/0.80 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> (((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))))),
% 0.80/0.80 inference(bind,[status(th)],[])).
% 0.80/0.80 tff(545,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.80/0.80 inference(quant_intro,[status(thm)],[544])).
% 0.80/0.80 tff(546,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_25')).
% 0.80/0.80 tff(547,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.80/0.80 tff(548,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[547, 543])).
% 0.80/0.80 tff(549,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[548, 541])).
% 0.80/0.80 tff(550,plain,(
% 0.80/0.80 ![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.80/0.80 inference(skolemize,[status(sab)],[549])).
% 0.80/0.80 tff(551,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[550, 540])).
% 0.80/0.80 tff(552,plain,
% 0.80/0.80 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(553,plain,
% 0.80/0.80 ((big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4))) <=> (big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(554,plain,
% 0.80/0.80 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4))))),
% 0.80/0.80 inference(monotonicity,[status(thm)],[553])).
% 0.80/0.80 tff(555,plain,
% 0.80/0.80 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.80/0.80 inference(transitivity,[status(thm)],[554, 552])).
% 0.80/0.80 tff(556,plain,
% 0.80/0.80 ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))),
% 0.80/0.80 inference(quant_inst,[status(thm)],[])).
% 0.80/0.80 tff(557,plain,
% 0.80/0.80 ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.80/0.80 tff(558,plain,
% 0.80/0.80 (big_p(f4(c2)) | big_r(c4, f1(c4))),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[557, 551, 517, 4, 516])).
% 0.80/0.80 tff(559,plain,
% 0.80/0.80 (big_r(c4, f1(c4))),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[558, 6])).
% 0.80/0.80 tff(560,plain,
% 0.80/0.80 (^[X7: $i, X8: $i, X1: $i] : refl((big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))),
% 0.80/0.80 inference(bind,[status(th)],[])).
% 0.80/0.80 tff(561,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.80 inference(quant_intro,[status(thm)],[560])).
% 0.80/0.80 tff(562,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(563,plain,
% 0.80/0.80 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ($false | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), rewrite(($false | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))))),
% 0.80/0.80 inference(bind,[status(th)],[])).
% 0.80/0.80 tff(564,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.80 inference(quant_intro,[status(thm)],[563])).
% 0.80/0.80 tff(565,plain,
% 0.80/0.80 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> (((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))))),
% 0.80/0.80 inference(bind,[status(th)],[])).
% 0.80/0.80 tff(566,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.80 inference(quant_intro,[status(thm)],[565])).
% 0.80/0.80 tff(567,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_31')).
% 0.80/0.80 tff(568,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.80/0.80 tff(569,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[568, 564])).
% 0.80/0.80 tff(570,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[569, 562])).
% 0.80/0.80 tff(571,plain,(
% 0.80/0.80 ![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.80 inference(skolemize,[status(sab)],[570])).
% 0.80/0.80 tff(572,plain,
% 0.80/0.80 (![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[571, 561])).
% 0.80/0.80 tff(573,plain,
% 0.80/0.80 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(574,plain,
% 0.80/0.80 ((big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4))) <=> (big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(575,plain,
% 0.80/0.80 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4))))),
% 0.80/0.80 inference(monotonicity,[status(thm)],[574])).
% 0.80/0.80 tff(576,plain,
% 0.80/0.80 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.80 inference(transitivity,[status(thm)],[575, 573])).
% 0.80/0.80 tff(577,plain,
% 0.80/0.80 ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))),
% 0.80/0.80 inference(quant_inst,[status(thm)],[])).
% 0.80/0.80 tff(578,plain,
% 0.80/0.80 ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.80/0.80 tff(579,plain,
% 0.80/0.80 (big_p(f4(c2)) | big_r(f1(c4), f2(c4))),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[578, 572, 517, 4, 516])).
% 0.80/0.80 tff(580,plain,
% 0.80/0.80 (big_r(f1(c4), f2(c4))),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[579, 6])).
% 0.80/0.80 tff(581,plain,
% 0.80/0.80 (^[X2: $i, X7: $i, X1: $i] : refl((big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))),
% 0.80/0.80 inference(bind,[status(th)],[])).
% 0.80/0.80 tff(582,plain,
% 0.80/0.80 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.80 inference(quant_intro,[status(thm)],[581])).
% 0.80/0.80 tff(583,plain,
% 0.80/0.80 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(584,plain,
% 0.80/0.80 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ($false | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), rewrite(($false | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))))),
% 0.80/0.80 inference(bind,[status(th)],[])).
% 0.80/0.80 tff(585,plain,
% 0.80/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.80 inference(quant_intro,[status(thm)],[584])).
% 0.80/0.80 tff(586,plain,
% 0.80/0.80 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> (((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_p(f6(X1))))), rewrite((((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))))),
% 0.80/0.81 inference(bind,[status(th)],[])).
% 0.80/0.81 tff(587,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(quant_intro,[status(thm)],[586])).
% 0.80/0.81 tff(588,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_16')).
% 0.80/0.81 tff(589,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.80/0.81 tff(590,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[589, 585])).
% 0.80/0.81 tff(591,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[590, 583])).
% 0.80/0.81 tff(592,plain,(
% 0.80/0.81 ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(skolemize,[status(sab)],[591])).
% 0.80/0.81 tff(593,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[592, 582])).
% 0.80/0.81 tff(594,plain,
% 0.80/0.81 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(595,plain,
% 0.80/0.81 ((big_p(c2) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c2), f2(c2))) <=> (big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(596,plain,
% 0.80/0.81 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4))))),
% 0.80/0.81 inference(monotonicity,[status(thm)],[595])).
% 0.80/0.81 tff(597,plain,
% 0.80/0.81 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))),
% 0.80/0.81 inference(transitivity,[status(thm)],[596, 594])).
% 0.80/0.81 tff(598,plain,
% 0.80/0.81 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c2), f2(c2)))),
% 0.80/0.81 inference(quant_inst,[status(thm)],[])).
% 0.80/0.81 tff(599,plain,
% 0.80/0.81 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[598, 597])).
% 0.80/0.81 tff(600,plain,
% 0.80/0.81 (big_r(f1(c2), f2(c2)) | (~big_p(c3)) | big_p(f6(c4))),
% 0.80/0.81 inference(unit_resolution,[status(thm)],[599, 593, 4, 516])).
% 0.80/0.81 tff(601,plain,
% 0.80/0.81 (big_p(f6(c4))),
% 0.80/0.81 inference(unit_resolution,[status(thm)],[600, 352, 517])).
% 0.80/0.81 tff(602,plain,
% 0.80/0.81 (^[X2: $i, X7: $i, X1: $i] : refl((big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7))) <=> (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7))))),
% 0.80/0.81 inference(bind,[status(th)],[])).
% 0.80/0.81 tff(603,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(quant_intro,[status(thm)],[602])).
% 0.80/0.81 tff(604,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(605,plain,
% 0.80/0.81 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7))) <=> ($false | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7))))), rewrite(($false | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7))) <=> (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))), (((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7))) <=> (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))))),
% 0.80/0.81 inference(bind,[status(th)],[])).
% 0.80/0.81 tff(606,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(quant_intro,[status(thm)],[605])).
% 0.80/0.81 tff(607,plain,
% 0.80/0.81 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> (((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(X1, f5(X1))))), rewrite((((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))))),
% 0.80/0.81 inference(bind,[status(th)],[])).
% 0.80/0.81 tff(608,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(quant_intro,[status(thm)],[607])).
% 0.80/0.81 tff(609,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_17')).
% 0.80/0.81 tff(610,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[609, 608])).
% 0.80/0.81 tff(611,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[610, 606])).
% 0.80/0.81 tff(612,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[611, 604])).
% 0.80/0.81 tff(613,plain,(
% 0.80/0.81 ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(skolemize,[status(sab)],[612])).
% 0.80/0.81 tff(614,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[613, 603])).
% 0.80/0.81 tff(615,plain,
% 0.80/0.81 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(616,plain,
% 0.80/0.81 ((big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4)) | big_r(f1(c2), f2(c2))) <=> (big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(617,plain,
% 0.80/0.81 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4))))),
% 0.80/0.81 inference(monotonicity,[status(thm)],[616])).
% 0.80/0.81 tff(618,plain,
% 0.80/0.81 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))),
% 0.80/0.81 inference(transitivity,[status(thm)],[617, 615])).
% 0.80/0.81 tff(619,plain,
% 0.80/0.81 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4)) | big_r(f1(c2), f2(c2)))),
% 0.80/0.81 inference(quant_inst,[status(thm)],[])).
% 0.80/0.81 tff(620,plain,
% 0.80/0.81 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.80/0.81 tff(621,plain,
% 0.80/0.81 (big_r(f1(c2), f2(c2)) | (~big_p(c3)) | big_r(c4, f5(c4))),
% 0.80/0.81 inference(unit_resolution,[status(thm)],[620, 614, 4, 516])).
% 0.80/0.81 tff(622,plain,
% 0.80/0.81 (big_r(c4, f5(c4))),
% 0.80/0.81 inference(unit_resolution,[status(thm)],[621, 352, 517])).
% 0.80/0.81 tff(623,plain,
% 0.80/0.81 (^[X2: $i, X7: $i, X1: $i] : refl((big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7))) <=> (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7))))),
% 0.80/0.81 inference(bind,[status(th)],[])).
% 0.80/0.81 tff(624,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(quant_intro,[status(thm)],[623])).
% 0.80/0.81 tff(625,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(626,plain,
% 0.80/0.81 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7))) <=> ($false | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7))))), rewrite(($false | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7))) <=> (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))), (((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7))) <=> (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))))),
% 0.80/0.81 inference(bind,[status(th)],[])).
% 0.80/0.81 tff(627,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(quant_intro,[status(thm)],[626])).
% 0.80/0.81 tff(628,plain,
% 0.80/0.81 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> (((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(f5(X1), f6(X1))))), rewrite((((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))))),
% 0.80/0.81 inference(bind,[status(th)],[])).
% 0.80/0.81 tff(629,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.81 inference(quant_intro,[status(thm)],[628])).
% 0.80/0.81 tff(630,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_18')).
% 0.80/0.81 tff(631,plain,
% 0.80/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.80/0.82 tff(632,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[631, 627])).
% 0.80/0.82 tff(633,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[632, 625])).
% 0.80/0.82 tff(634,plain,(
% 0.80/0.82 ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.82 inference(skolemize,[status(sab)],[633])).
% 0.80/0.82 tff(635,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[634, 624])).
% 0.80/0.82 tff(636,plain,
% 0.80/0.82 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(637,plain,
% 0.80/0.82 ((big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4)) | big_r(f1(c2), f2(c2))) <=> (big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(638,plain,
% 0.80/0.82 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4))))),
% 0.80/0.82 inference(monotonicity,[status(thm)],[637])).
% 0.80/0.82 tff(639,plain,
% 0.80/0.82 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))),
% 0.80/0.82 inference(transitivity,[status(thm)],[638, 636])).
% 0.80/0.82 tff(640,plain,
% 0.80/0.82 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4)) | big_r(f1(c2), f2(c2)))),
% 0.80/0.82 inference(quant_inst,[status(thm)],[])).
% 0.80/0.82 tff(641,plain,
% 0.80/0.82 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[640, 639])).
% 0.80/0.82 tff(642,plain,
% 0.80/0.82 (big_r(f1(c2), f2(c2)) | (~big_p(c3)) | big_r(f5(c4), f6(c4))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[641, 635, 4, 516])).
% 0.80/0.82 tff(643,plain,
% 0.80/0.82 (big_r(f5(c4), f6(c4))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[642, 352, 517])).
% 0.80/0.82 tff(644,plain,
% 0.80/0.82 (big_r(c2, f3(c2))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[219, 352])).
% 0.80/0.82 tff(645,plain,
% 0.80/0.82 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(646,plain,
% 0.80/0.82 (((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2)))) <=> ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(647,plain,
% 0.80/0.82 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4)))))),
% 0.80/0.82 inference(monotonicity,[status(thm)],[646])).
% 0.80/0.82 tff(648,plain,
% 0.80/0.82 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.80/0.82 inference(transitivity,[status(thm)],[647, 645])).
% 0.80/0.82 tff(649,plain,
% 0.80/0.82 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))),
% 0.80/0.82 inference(quant_inst,[status(thm)],[])).
% 0.80/0.82 tff(650,plain,
% 0.80/0.82 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4)))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[649, 648])).
% 0.80/0.82 tff(651,plain,
% 0.80/0.82 (~big_p(f4(c2))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[650, 196, 644, 475, 643, 622, 601])).
% 0.80/0.82 tff(652,plain,
% 0.80/0.82 ($false),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[358, 271, 4, 352, 651])).
% 0.80/0.82 tff(653,plain,(big_r(f1(c2), f2(c2)) | big_p(c2) | (~big_p(c3)) | (~big_r(c4, c3))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.82 tff(654,plain,
% 0.80/0.82 (big_r(f1(c2), f2(c2))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[653, 4, 517, 516])).
% 0.80/0.82 tff(655,plain,
% 0.80/0.82 (^[X2: $i, X7: $i, X1: $i] : refl((big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.80/0.82 inference(bind,[status(th)],[])).
% 0.80/0.82 tff(656,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.80/0.82 inference(quant_intro,[status(thm)],[655])).
% 0.80/0.82 tff(657,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(658,plain,
% 0.80/0.82 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ($false | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))))), rewrite(($false | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.80/0.82 inference(bind,[status(th)],[])).
% 0.80/0.82 tff(659,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.80/0.82 inference(quant_intro,[status(thm)],[658])).
% 0.80/0.82 tff(660,plain,
% 0.80/0.82 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2)))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), ((((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.80/0.82 inference(bind,[status(th)],[])).
% 0.80/0.82 tff(661,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.80/0.82 inference(quant_intro,[status(thm)],[660])).
% 0.80/0.82 tff(662,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_10')).
% 0.80/0.82 tff(663,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.80/0.82 tff(664,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[663, 659])).
% 0.80/0.82 tff(665,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[664, 657])).
% 0.80/0.82 tff(666,plain,(
% 0.80/0.82 ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.80/0.82 inference(skolemize,[status(sab)],[665])).
% 0.80/0.82 tff(667,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[666, 656])).
% 0.80/0.82 tff(668,plain,
% 0.80/0.82 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(669,plain,
% 0.80/0.82 ((big_p(c2) | big_r(c2, f1(c2)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> (big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(670,plain,
% 0.80/0.82 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(c2) | big_r(c2, f1(c2)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4))))),
% 0.80/0.82 inference(monotonicity,[status(thm)],[669])).
% 0.80/0.82 tff(671,plain,
% 0.80/0.82 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(c2) | big_r(c2, f1(c2)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))),
% 0.80/0.82 inference(transitivity,[status(thm)],[670, 668])).
% 0.80/0.82 tff(672,plain,
% 0.80/0.82 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(c2) | big_r(c2, f1(c2)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.80/0.82 inference(quant_inst,[status(thm)],[])).
% 0.80/0.82 tff(673,plain,
% 0.80/0.82 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.80/0.82 tff(674,plain,
% 0.80/0.82 (big_r(c2, f1(c2)) | (~big_p(c3)) | big_p(f6(c4))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[673, 667, 4, 516])).
% 0.80/0.82 tff(675,plain,
% 0.80/0.82 (big_p(f6(c4))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[674, 1, 517])).
% 0.80/0.82 tff(676,plain,
% 0.80/0.82 (^[X2: $i, X7: $i, X1: $i] : refl((big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))))),
% 0.80/0.82 inference(bind,[status(th)],[])).
% 0.80/0.82 tff(677,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.80/0.82 inference(quant_intro,[status(thm)],[676])).
% 0.80/0.82 tff(678,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(679,plain,
% 0.80/0.82 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> ($false | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))))), rewrite(($false | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))), (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))))),
% 0.80/0.82 inference(bind,[status(th)],[])).
% 0.80/0.82 tff(680,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.80/0.82 inference(quant_intro,[status(thm)],[679])).
% 0.80/0.82 tff(681,plain,
% 0.80/0.82 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2)))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), ((((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))), ((((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))))),
% 0.80/0.82 inference(bind,[status(th)],[])).
% 0.80/0.82 tff(682,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.80/0.82 inference(quant_intro,[status(thm)],[681])).
% 0.80/0.82 tff(683,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_11')).
% 0.80/0.82 tff(684,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.80/0.82 tff(685,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[684, 680])).
% 0.80/0.82 tff(686,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[685, 678])).
% 0.80/0.82 tff(687,plain,(
% 0.80/0.82 ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.80/0.82 inference(skolemize,[status(sab)],[686])).
% 0.80/0.82 tff(688,plain,
% 0.80/0.82 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[687, 677])).
% 0.80/0.82 tff(689,plain,
% 0.80/0.82 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(690,plain,
% 0.80/0.82 ((big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4))) <=> (big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(691,plain,
% 0.80/0.82 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4))))),
% 0.80/0.82 inference(monotonicity,[status(thm)],[690])).
% 0.80/0.82 tff(692,plain,
% 0.80/0.82 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))),
% 0.80/0.83 inference(transitivity,[status(thm)],[691, 689])).
% 0.80/0.83 tff(693,plain,
% 0.80/0.83 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4)))),
% 0.80/0.83 inference(quant_inst,[status(thm)],[])).
% 0.80/0.83 tff(694,plain,
% 0.80/0.83 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4))),
% 0.80/0.83 inference(modus_ponens,[status(thm)],[693, 692])).
% 0.80/0.83 tff(695,plain,
% 0.80/0.83 (big_r(c2, f1(c2)) | (~big_p(c3)) | big_r(c4, f5(c4))),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[694, 688, 4, 516])).
% 0.80/0.83 tff(696,plain,
% 0.80/0.83 (big_r(c4, f5(c4))),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[695, 1, 517])).
% 0.80/0.83 tff(697,plain,
% 0.80/0.83 (^[X2: $i, X7: $i, X1: $i] : refl((big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))))),
% 0.80/0.83 inference(bind,[status(th)],[])).
% 0.80/0.83 tff(698,plain,
% 0.80/0.83 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.80/0.83 inference(quant_intro,[status(thm)],[697])).
% 0.80/0.83 tff(699,plain,
% 0.80/0.83 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.80/0.83 inference(rewrite,[status(thm)],[])).
% 0.80/0.83 tff(700,plain,
% 0.80/0.83 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> ($false | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))))), rewrite(($false | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))), (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))))),
% 0.80/0.83 inference(bind,[status(th)],[])).
% 0.80/0.83 tff(701,plain,
% 0.80/0.83 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.80/0.83 inference(quant_intro,[status(thm)],[700])).
% 0.80/0.83 tff(702,plain,
% 0.80/0.83 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2)))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), ((((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))), ((((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))))),
% 0.80/0.83 inference(bind,[status(th)],[])).
% 0.80/0.83 tff(703,plain,
% 0.80/0.83 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.80/0.83 inference(quant_intro,[status(thm)],[702])).
% 0.80/0.83 tff(704,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_12')).
% 0.80/0.83 tff(705,plain,
% 0.80/0.83 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.80/0.83 inference(modus_ponens,[status(thm)],[704, 703])).
% 0.80/0.83 tff(706,plain,
% 0.80/0.83 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.80/0.83 inference(modus_ponens,[status(thm)],[705, 701])).
% 0.80/0.83 tff(707,plain,
% 0.80/0.83 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.80/0.83 inference(modus_ponens,[status(thm)],[706, 699])).
% 0.80/0.83 tff(708,plain,(
% 0.80/0.83 ![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.80/0.83 inference(skolemize,[status(sab)],[707])).
% 0.80/0.83 tff(709,plain,
% 0.80/0.83 (![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.80/0.83 inference(modus_ponens,[status(thm)],[708, 698])).
% 0.80/0.83 tff(710,plain,
% 0.80/0.83 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))),
% 0.80/0.83 inference(rewrite,[status(thm)],[])).
% 0.80/0.83 tff(711,plain,
% 0.80/0.83 ((big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4))) <=> (big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))),
% 0.80/0.83 inference(rewrite,[status(thm)],[])).
% 0.80/0.83 tff(712,plain,
% 0.80/0.83 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4))))),
% 0.80/0.83 inference(monotonicity,[status(thm)],[711])).
% 0.80/0.83 tff(713,plain,
% 0.80/0.83 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))),
% 0.80/0.83 inference(transitivity,[status(thm)],[712, 710])).
% 0.80/0.83 tff(714,plain,
% 0.80/0.83 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4)))),
% 0.80/0.83 inference(quant_inst,[status(thm)],[])).
% 0.80/0.83 tff(715,plain,
% 0.80/0.83 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4))),
% 0.80/0.83 inference(modus_ponens,[status(thm)],[714, 713])).
% 0.80/0.83 tff(716,plain,
% 0.80/0.83 (big_r(c2, f1(c2)) | (~big_p(c3)) | big_r(f5(c4), f6(c4))),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[715, 709, 4, 516])).
% 0.80/0.83 tff(717,plain,
% 0.80/0.83 (big_r(f5(c4), f6(c4))),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[716, 1, 517])).
% 0.80/0.83 tff(718,plain,
% 0.80/0.83 (big_r(c2, f3(c2)) | big_p(f2(c2))),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[118, 112, 4])).
% 0.80/0.83 tff(719,plain,
% 0.80/0.83 (big_p(f2(c2))),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[718, 99])).
% 0.80/0.83 tff(720,plain,
% 0.80/0.83 (^[X7: $i, X8: $i, X1: $i] : refl((big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))),
% 0.80/0.83 inference(bind,[status(th)],[])).
% 0.80/0.83 tff(721,plain,
% 0.80/0.83 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.80/0.83 inference(quant_intro,[status(thm)],[720])).
% 0.80/0.83 tff(722,plain,
% 0.80/0.83 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.80/0.83 inference(rewrite,[status(thm)],[])).
% 0.80/0.83 tff(723,plain,
% 0.80/0.83 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ($false | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), rewrite(($false | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))))),
% 0.87/0.83 inference(bind,[status(th)],[])).
% 0.87/0.83 tff(724,plain,
% 0.87/0.83 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.83 inference(quant_intro,[status(thm)],[723])).
% 0.87/0.83 tff(725,plain,
% 0.87/0.83 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X1, f3(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))))),
% 0.87/0.83 inference(bind,[status(th)],[])).
% 0.87/0.83 tff(726,plain,
% 0.87/0.83 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.83 inference(quant_intro,[status(thm)],[725])).
% 0.87/0.83 tff(727,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_20')).
% 0.87/0.83 tff(728,plain,
% 0.87/0.83 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[727, 726])).
% 0.87/0.83 tff(729,plain,
% 0.87/0.83 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[728, 724])).
% 0.87/0.83 tff(730,plain,
% 0.87/0.83 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[729, 722])).
% 0.87/0.83 tff(731,plain,(
% 0.87/0.83 ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.83 inference(skolemize,[status(sab)],[730])).
% 0.87/0.83 tff(732,plain,
% 0.87/0.83 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[731, 721])).
% 0.87/0.83 tff(733,plain,
% 0.87/0.83 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.87/0.83 inference(rewrite,[status(thm)],[])).
% 0.87/0.83 tff(734,plain,
% 0.87/0.83 ((big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> (big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.87/0.83 inference(rewrite,[status(thm)],[])).
% 0.87/0.83 tff(735,plain,
% 0.87/0.83 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4))))),
% 0.87/0.83 inference(monotonicity,[status(thm)],[734])).
% 0.87/0.83 tff(736,plain,
% 0.87/0.83 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.87/0.83 inference(transitivity,[status(thm)],[735, 733])).
% 0.87/0.83 tff(737,plain,
% 0.87/0.83 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.87/0.83 inference(quant_inst,[status(thm)],[])).
% 0.87/0.83 tff(738,plain,
% 0.87/0.83 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4))),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.87/0.83 tff(739,plain,
% 0.87/0.83 (big_r(c2, f3(c2)) | (~big_p(c3)) | big_p(f2(c4))),
% 0.87/0.83 inference(unit_resolution,[status(thm)],[738, 732, 4, 516])).
% 0.87/0.83 tff(740,plain,
% 0.87/0.83 (big_p(f2(c4))),
% 0.87/0.83 inference(unit_resolution,[status(thm)],[739, 99, 517])).
% 0.87/0.83 tff(741,plain,
% 0.87/0.83 (^[X7: $i, X8: $i, X1: $i] : refl((big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))),
% 0.87/0.83 inference(bind,[status(th)],[])).
% 0.87/0.83 tff(742,plain,
% 0.87/0.83 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.83 inference(quant_intro,[status(thm)],[741])).
% 0.87/0.83 tff(743,plain,
% 0.87/0.83 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.83 inference(rewrite,[status(thm)],[])).
% 0.87/0.83 tff(744,plain,
% 0.87/0.83 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ($false | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), rewrite(($false | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))))),
% 0.87/0.83 inference(bind,[status(th)],[])).
% 0.87/0.83 tff(745,plain,
% 0.87/0.83 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.83 inference(quant_intro,[status(thm)],[744])).
% 0.87/0.83 tff(746,plain,
% 0.87/0.83 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> (((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_r(X1, f3(X1))))), rewrite((((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))))),
% 0.87/0.83 inference(bind,[status(th)],[])).
% 0.87/0.83 tff(747,plain,
% 0.87/0.83 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.83 inference(quant_intro,[status(thm)],[746])).
% 0.87/0.83 tff(748,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_26')).
% 0.87/0.83 tff(749,plain,
% 0.87/0.83 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[748, 747])).
% 0.87/0.84 tff(750,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[749, 745])).
% 0.87/0.84 tff(751,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[750, 743])).
% 0.87/0.84 tff(752,plain,(
% 0.87/0.84 ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.84 inference(skolemize,[status(sab)],[751])).
% 0.87/0.84 tff(753,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[752, 742])).
% 0.87/0.84 tff(754,plain,
% 0.87/0.84 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.87/0.84 inference(rewrite,[status(thm)],[])).
% 0.87/0.84 tff(755,plain,
% 0.87/0.84 ((big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4))) <=> (big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.87/0.84 inference(rewrite,[status(thm)],[])).
% 0.87/0.84 tff(756,plain,
% 0.87/0.84 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4))))),
% 0.87/0.84 inference(monotonicity,[status(thm)],[755])).
% 0.87/0.84 tff(757,plain,
% 0.87/0.84 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.87/0.84 inference(transitivity,[status(thm)],[756, 754])).
% 0.87/0.84 tff(758,plain,
% 0.87/0.84 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))),
% 0.87/0.84 inference(quant_inst,[status(thm)],[])).
% 0.87/0.84 tff(759,plain,
% 0.87/0.84 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[758, 757])).
% 0.87/0.84 tff(760,plain,
% 0.87/0.84 (big_r(c2, f3(c2)) | (~big_p(c3)) | big_r(c4, f1(c4))),
% 0.87/0.84 inference(unit_resolution,[status(thm)],[759, 753, 4, 516])).
% 0.87/0.84 tff(761,plain,
% 0.87/0.84 (big_r(c4, f1(c4))),
% 0.87/0.84 inference(unit_resolution,[status(thm)],[760, 99, 517])).
% 0.87/0.84 tff(762,plain,
% 0.87/0.84 (^[X7: $i, X8: $i, X1: $i] : refl((big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))),
% 0.87/0.84 inference(bind,[status(th)],[])).
% 0.87/0.84 tff(763,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.84 inference(quant_intro,[status(thm)],[762])).
% 0.87/0.84 tff(764,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.84 inference(rewrite,[status(thm)],[])).
% 0.87/0.84 tff(765,plain,
% 0.87/0.84 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ($false | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), rewrite(($false | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))))),
% 0.87/0.84 inference(bind,[status(th)],[])).
% 0.87/0.84 tff(766,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.84 inference(quant_intro,[status(thm)],[765])).
% 0.87/0.84 tff(767,plain,
% 0.87/0.84 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> (((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_r(X1, f3(X1))))), rewrite((((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))))),
% 0.87/0.84 inference(bind,[status(th)],[])).
% 0.87/0.84 tff(768,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.84 inference(quant_intro,[status(thm)],[767])).
% 0.87/0.84 tff(769,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_32')).
% 0.87/0.84 tff(770,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[769, 768])).
% 0.87/0.84 tff(771,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[770, 766])).
% 0.87/0.84 tff(772,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[771, 764])).
% 0.87/0.84 tff(773,plain,(
% 0.87/0.84 ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.84 inference(skolemize,[status(sab)],[772])).
% 0.87/0.84 tff(774,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[773, 763])).
% 0.87/0.84 tff(775,plain,
% 0.87/0.84 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.87/0.84 inference(rewrite,[status(thm)],[])).
% 0.87/0.84 tff(776,plain,
% 0.87/0.84 ((big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4))) <=> (big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.87/0.84 inference(rewrite,[status(thm)],[])).
% 0.87/0.84 tff(777,plain,
% 0.87/0.84 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4))))),
% 0.87/0.84 inference(monotonicity,[status(thm)],[776])).
% 0.87/0.84 tff(778,plain,
% 0.87/0.84 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.87/0.84 inference(transitivity,[status(thm)],[777, 775])).
% 0.87/0.84 tff(779,plain,
% 0.87/0.84 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))),
% 0.87/0.84 inference(quant_inst,[status(thm)],[])).
% 0.87/0.84 tff(780,plain,
% 0.87/0.84 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[779, 778])).
% 0.87/0.84 tff(781,plain,
% 0.87/0.84 (big_r(c2, f3(c2)) | (~big_p(c3)) | big_r(f1(c4), f2(c4))),
% 0.87/0.84 inference(unit_resolution,[status(thm)],[780, 774, 4, 516])).
% 0.87/0.84 tff(782,plain,
% 0.87/0.84 (big_r(f1(c4), f2(c4))),
% 0.87/0.84 inference(unit_resolution,[status(thm)],[781, 99, 517])).
% 0.87/0.84 tff(783,plain,
% 0.87/0.84 ($false),
% 0.87/0.84 inference(unit_resolution,[status(thm)],[226, 196, 432, 654, 782, 761, 740, 719])).
% 0.87/0.84 tff(784,plain,(big_r(c2, f3(c2)) | big_p(c2) | (~big_p(c3)) | (~big_r(c4, c3))), inference(lemma,lemma(discharge,[]))).
% 0.87/0.84 tff(785,plain,
% 0.87/0.84 (big_r(c2, f3(c2))),
% 0.87/0.84 inference(unit_resolution,[status(thm)],[784, 4, 517, 516])).
% 0.87/0.84 tff(786,plain,
% 0.87/0.84 (~big_p(f4(c2))),
% 0.87/0.84 inference(unit_resolution,[status(thm)],[650, 196, 785, 186, 717, 696, 675])).
% 0.87/0.84 tff(787,plain,
% 0.87/0.84 ($false),
% 0.87/0.84 inference(unit_resolution,[status(thm)],[169, 48, 4, 1, 786])).
% 0.87/0.84 tff(788,plain,(big_r(c2, f1(c2)) | big_p(c2) | (~big_p(c3)) | (~big_r(c4, c3))), inference(lemma,lemma(discharge,[]))).
% 0.87/0.84 tff(789,plain,
% 0.87/0.84 (big_r(c2, f1(c2))),
% 0.87/0.84 inference(unit_resolution,[status(thm)],[788, 4, 517, 516])).
% 0.87/0.84 tff(790,plain,
% 0.87/0.84 ($false),
% 0.87/0.84 inference(unit_resolution,[status(thm)],[226, 196, 789, 654, 580, 559, 538, 35])).
% 0.87/0.84 tff(791,plain,(big_p(f4(c2)) | big_p(c2) | (~big_p(c3)) | (~big_r(c4, c3))), inference(lemma,lemma(discharge,[]))).
% 0.87/0.84 tff(792,plain,
% 0.87/0.84 (big_p(f4(c2))),
% 0.87/0.84 inference(unit_resolution,[status(thm)],[791, 4, 515, 516])).
% 0.87/0.84 tff(793,plain,
% 0.87/0.84 (^[X7: $i, X8: $i, X1: $i] : refl((big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))),
% 0.87/0.84 inference(bind,[status(th)],[])).
% 0.87/0.84 tff(794,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.84 inference(quant_intro,[status(thm)],[793])).
% 0.87/0.84 tff(795,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.84 inference(rewrite,[status(thm)],[])).
% 0.87/0.84 tff(796,plain,
% 0.87/0.84 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ($false | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), rewrite(($false | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))))),
% 0.87/0.84 inference(bind,[status(th)],[])).
% 0.87/0.84 tff(797,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.84 inference(quant_intro,[status(thm)],[796])).
% 0.87/0.84 tff(798,plain,
% 0.87/0.84 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f3(X1), f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))))),
% 0.87/0.84 inference(bind,[status(th)],[])).
% 0.87/0.84 tff(799,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.84 inference(quant_intro,[status(thm)],[798])).
% 0.87/0.84 tff(800,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_21')).
% 0.87/0.84 tff(801,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[800, 799])).
% 0.87/0.84 tff(802,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[801, 797])).
% 0.87/0.84 tff(803,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[802, 795])).
% 0.87/0.84 tff(804,plain,(
% 0.87/0.84 ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.84 inference(skolemize,[status(sab)],[803])).
% 0.87/0.84 tff(805,plain,
% 0.87/0.84 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[804, 794])).
% 0.87/0.84 tff(806,plain,
% 0.87/0.84 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.87/0.84 inference(rewrite,[status(thm)],[])).
% 0.87/0.84 tff(807,plain,
% 0.87/0.84 ((big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.87/0.84 inference(rewrite,[status(thm)],[])).
% 0.87/0.84 tff(808,plain,
% 0.87/0.84 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4))))),
% 0.87/0.84 inference(monotonicity,[status(thm)],[807])).
% 0.87/0.84 tff(809,plain,
% 0.87/0.84 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.87/0.85 inference(transitivity,[status(thm)],[808, 806])).
% 0.87/0.85 tff(810,plain,
% 0.87/0.85 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.87/0.85 inference(quant_inst,[status(thm)],[])).
% 0.87/0.85 tff(811,plain,
% 0.87/0.85 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[810, 809])).
% 0.87/0.85 tff(812,plain,
% 0.87/0.85 (big_r(f3(c2), f4(c2)) | (~big_p(c3)) | big_p(f2(c4))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[811, 805, 4, 516])).
% 0.87/0.85 tff(813,plain,
% 0.87/0.85 (big_p(f2(c4))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[812, 231, 517])).
% 0.87/0.85 tff(814,plain,
% 0.87/0.85 (^[X7: $i, X8: $i, X1: $i] : refl((big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))),
% 0.87/0.85 inference(bind,[status(th)],[])).
% 0.87/0.85 tff(815,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.85 inference(quant_intro,[status(thm)],[814])).
% 0.87/0.85 tff(816,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.85 inference(rewrite,[status(thm)],[])).
% 0.87/0.85 tff(817,plain,
% 0.87/0.85 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ($false | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), rewrite(($false | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))))),
% 0.87/0.85 inference(bind,[status(th)],[])).
% 0.87/0.85 tff(818,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.85 inference(quant_intro,[status(thm)],[817])).
% 0.87/0.85 tff(819,plain,
% 0.87/0.85 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> (((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_r(f3(X1), f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))))),
% 0.87/0.85 inference(bind,[status(th)],[])).
% 0.87/0.85 tff(820,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.85 inference(quant_intro,[status(thm)],[819])).
% 0.87/0.85 tff(821,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_27')).
% 0.87/0.85 tff(822,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[821, 820])).
% 0.87/0.85 tff(823,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[822, 818])).
% 0.87/0.85 tff(824,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[823, 816])).
% 0.87/0.85 tff(825,plain,(
% 0.87/0.85 ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.85 inference(skolemize,[status(sab)],[824])).
% 0.87/0.85 tff(826,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[825, 815])).
% 0.87/0.85 tff(827,plain,
% 0.87/0.85 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.87/0.85 inference(rewrite,[status(thm)],[])).
% 0.87/0.85 tff(828,plain,
% 0.87/0.85 ((big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4))) <=> (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.87/0.85 inference(rewrite,[status(thm)],[])).
% 0.87/0.85 tff(829,plain,
% 0.87/0.85 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4))))),
% 0.87/0.85 inference(monotonicity,[status(thm)],[828])).
% 0.87/0.85 tff(830,plain,
% 0.87/0.85 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.87/0.85 inference(transitivity,[status(thm)],[829, 827])).
% 0.87/0.85 tff(831,plain,
% 0.87/0.85 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))),
% 0.87/0.85 inference(quant_inst,[status(thm)],[])).
% 0.87/0.85 tff(832,plain,
% 0.87/0.85 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[831, 830])).
% 0.87/0.85 tff(833,plain,
% 0.87/0.85 (big_r(f3(c2), f4(c2)) | (~big_p(c3)) | big_r(c4, f1(c4))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[832, 826, 4, 516])).
% 0.87/0.85 tff(834,plain,
% 0.87/0.85 (big_r(c4, f1(c4))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[833, 231, 517])).
% 0.87/0.85 tff(835,plain,
% 0.87/0.85 (^[X7: $i, X8: $i, X1: $i] : refl((big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))),
% 0.87/0.85 inference(bind,[status(th)],[])).
% 0.87/0.85 tff(836,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.85 inference(quant_intro,[status(thm)],[835])).
% 0.87/0.85 tff(837,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.85 inference(rewrite,[status(thm)],[])).
% 0.87/0.85 tff(838,plain,
% 0.87/0.85 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ($false | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), rewrite(($false | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))))),
% 0.87/0.85 inference(bind,[status(th)],[])).
% 0.87/0.85 tff(839,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.85 inference(quant_intro,[status(thm)],[838])).
% 0.87/0.85 tff(840,plain,
% 0.87/0.85 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> (((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_r(f3(X1), f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))))),
% 0.87/0.85 inference(bind,[status(th)],[])).
% 0.87/0.85 tff(841,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.85 inference(quant_intro,[status(thm)],[840])).
% 0.87/0.85 tff(842,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_33')).
% 0.87/0.85 tff(843,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[842, 841])).
% 0.87/0.85 tff(844,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[843, 839])).
% 0.87/0.85 tff(845,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[844, 837])).
% 0.87/0.85 tff(846,plain,(
% 0.87/0.85 ![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.85 inference(skolemize,[status(sab)],[845])).
% 0.87/0.85 tff(847,plain,
% 0.87/0.85 (![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[846, 836])).
% 0.87/0.85 tff(848,plain,
% 0.87/0.85 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.87/0.85 inference(rewrite,[status(thm)],[])).
% 0.87/0.85 tff(849,plain,
% 0.87/0.85 ((big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4))) <=> (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.87/0.85 inference(rewrite,[status(thm)],[])).
% 0.87/0.85 tff(850,plain,
% 0.87/0.85 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4))))),
% 0.87/0.85 inference(monotonicity,[status(thm)],[849])).
% 0.87/0.85 tff(851,plain,
% 0.87/0.85 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.87/0.85 inference(transitivity,[status(thm)],[850, 848])).
% 0.87/0.85 tff(852,plain,
% 0.87/0.85 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))),
% 0.87/0.85 inference(quant_inst,[status(thm)],[])).
% 0.87/0.85 tff(853,plain,
% 0.87/0.85 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.87/0.85 tff(854,plain,
% 0.87/0.85 (big_r(f3(c2), f4(c2)) | (~big_p(c3)) | big_r(f1(c4), f2(c4))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[853, 847, 4, 516])).
% 0.87/0.85 tff(855,plain,
% 0.87/0.85 (big_r(f1(c4), f2(c4))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[854, 231, 517])).
% 0.87/0.85 tff(856,plain,
% 0.87/0.85 ($false),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[226, 196, 789, 654, 855, 834, 813, 474])).
% 0.87/0.85 tff(857,plain,(big_r(f3(c2), f4(c2)) | big_p(c2) | (~big_p(c3)) | (~big_r(c4, c3))), inference(lemma,lemma(discharge,[]))).
% 0.87/0.85 tff(858,plain,
% 0.87/0.85 (big_r(f3(c2), f4(c2))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[857, 4, 515, 516])).
% 0.87/0.85 tff(859,plain,
% 0.87/0.85 (big_r(c2, f3(c2))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[784, 4, 515, 516])).
% 0.87/0.85 tff(860,assumption,(~big_p(f2(c4))), introduced(assumption)).
% 0.87/0.85 tff(861,plain,
% 0.87/0.85 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl((big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.87/0.85 inference(bind,[status(th)],[])).
% 0.87/0.85 tff(862,plain,
% 0.87/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.85 inference(quant_intro,[status(thm)],[861])).
% 0.87/0.85 tff(863,plain,
% 0.87/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.85 inference(rewrite,[status(thm)],[])).
% 0.87/0.85 tff(864,plain,
% 0.87/0.85 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ($false | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))), rewrite(($false | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.87/0.85 inference(bind,[status(th)],[])).
% 0.87/0.85 tff(865,plain,
% 0.87/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.85 inference(quant_intro,[status(thm)],[864])).
% 0.87/0.85 tff(866,plain,
% 0.87/0.85 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.87/0.85 inference(bind,[status(th)],[])).
% 0.87/0.85 tff(867,plain,
% 0.87/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.85 inference(quant_intro,[status(thm)],[866])).
% 0.87/0.85 tff(868,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_22')).
% 0.87/0.85 tff(869,plain,
% 0.87/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[868, 867])).
% 0.87/0.85 tff(870,plain,
% 0.87/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[869, 865])).
% 0.87/0.85 tff(871,plain,
% 0.87/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[870, 863])).
% 0.87/0.85 tff(872,plain,(
% 0.87/0.85 ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.85 inference(skolemize,[status(sab)],[871])).
% 0.87/0.85 tff(873,plain,
% 0.87/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[872, 862])).
% 0.87/0.85 tff(874,plain,
% 0.87/0.85 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)) | big_p(f2(c4)))),
% 0.87/0.86 inference(rewrite,[status(thm)],[])).
% 0.87/0.86 tff(875,plain,
% 0.87/0.86 ((big_p(f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)) | big_p(f2(c4)))),
% 0.87/0.86 inference(rewrite,[status(thm)],[])).
% 0.87/0.86 tff(876,plain,
% 0.87/0.86 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)) | big_p(f2(c4))))),
% 0.87/0.86 inference(monotonicity,[status(thm)],[875])).
% 0.87/0.86 tff(877,plain,
% 0.87/0.86 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)) | big_p(f2(c4)))),
% 0.87/0.86 inference(transitivity,[status(thm)],[876, 874])).
% 0.87/0.86 tff(878,plain,
% 0.87/0.86 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.87/0.86 inference(quant_inst,[status(thm)],[])).
% 0.87/0.86 tff(879,plain,
% 0.87/0.86 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)) | big_p(f2(c4))),
% 0.87/0.86 inference(modus_ponens,[status(thm)],[878, 877])).
% 0.87/0.86 tff(880,plain,
% 0.87/0.86 ((~big_p(c3)) | big_p(f6(c4)) | big_p(f2(c4))),
% 0.87/0.86 inference(unit_resolution,[status(thm)],[879, 873, 516])).
% 0.87/0.86 tff(881,plain,
% 0.87/0.86 (big_p(f6(c4))),
% 0.87/0.86 inference(unit_resolution,[status(thm)],[880, 860, 517])).
% 0.87/0.86 tff(882,plain,
% 0.87/0.86 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl((big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.87/0.86 inference(bind,[status(th)],[])).
% 0.87/0.86 tff(883,plain,
% 0.87/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.86 inference(quant_intro,[status(thm)],[882])).
% 0.87/0.86 tff(884,plain,
% 0.87/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.86 inference(rewrite,[status(thm)],[])).
% 0.87/0.86 tff(885,plain,
% 0.87/0.86 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ($false | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))), rewrite(($false | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.87/0.86 inference(bind,[status(th)],[])).
% 0.87/0.86 tff(886,plain,
% 0.87/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.86 inference(quant_intro,[status(thm)],[885])).
% 0.87/0.86 tff(887,plain,
% 0.87/0.86 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.87/0.86 inference(bind,[status(th)],[])).
% 0.87/0.86 tff(888,plain,
% 0.87/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.86 inference(quant_intro,[status(thm)],[887])).
% 0.87/0.86 tff(889,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_23')).
% 0.87/0.86 tff(890,plain,
% 0.87/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.86 inference(modus_ponens,[status(thm)],[889, 888])).
% 0.87/0.86 tff(891,plain,
% 0.87/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.86 inference(modus_ponens,[status(thm)],[890, 886])).
% 0.87/0.86 tff(892,plain,
% 0.87/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.86 inference(modus_ponens,[status(thm)],[891, 884])).
% 0.87/0.86 tff(893,plain,(
% 0.87/0.86 ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.86 inference(skolemize,[status(sab)],[892])).
% 0.87/0.86 tff(894,plain,
% 0.87/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.86 inference(modus_ponens,[status(thm)],[893, 883])).
% 0.87/0.86 tff(895,plain,
% 0.87/0.86 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)) | big_p(f2(c4)))),
% 0.87/0.86 inference(rewrite,[status(thm)],[])).
% 0.87/0.86 tff(896,plain,
% 0.87/0.86 ((big_r(c4, f5(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)) | big_p(f2(c4)))),
% 0.87/0.86 inference(rewrite,[status(thm)],[])).
% 0.87/0.86 tff(897,plain,
% 0.87/0.86 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c4, f5(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)) | big_p(f2(c4))))),
% 0.87/0.86 inference(monotonicity,[status(thm)],[896])).
% 0.87/0.86 tff(898,plain,
% 0.87/0.86 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c4, f5(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)) | big_p(f2(c4)))),
% 0.87/0.86 inference(transitivity,[status(thm)],[897, 895])).
% 0.87/0.86 tff(899,plain,
% 0.87/0.86 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c4, f5(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.87/0.86 inference(quant_inst,[status(thm)],[])).
% 0.87/0.86 tff(900,plain,
% 0.87/0.86 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)) | big_p(f2(c4))),
% 0.87/0.86 inference(modus_ponens,[status(thm)],[899, 898])).
% 0.87/0.86 tff(901,plain,
% 0.87/0.86 ((~big_p(c3)) | big_r(c4, f5(c4)) | big_p(f2(c4))),
% 0.87/0.86 inference(unit_resolution,[status(thm)],[900, 894, 516])).
% 0.87/0.86 tff(902,plain,
% 0.87/0.86 (big_r(c4, f5(c4))),
% 0.87/0.86 inference(unit_resolution,[status(thm)],[901, 860, 517])).
% 0.87/0.86 tff(903,plain,
% 0.87/0.86 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl((big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.87/0.86 inference(bind,[status(th)],[])).
% 0.87/0.86 tff(904,plain,
% 0.87/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.86 inference(quant_intro,[status(thm)],[903])).
% 0.87/0.86 tff(905,plain,
% 0.87/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.86 inference(rewrite,[status(thm)],[])).
% 0.87/0.86 tff(906,plain,
% 0.87/0.86 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ($false | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))), rewrite(($false | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.87/0.86 inference(bind,[status(th)],[])).
% 0.87/0.86 tff(907,plain,
% 0.87/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.87/0.86 inference(quant_intro,[status(thm)],[906])).
% 0.87/0.86 tff(908,plain,
% 0.87/0.86 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.90/0.86 inference(bind,[status(th)],[])).
% 0.90/0.86 tff(909,plain,
% 0.90/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.86 inference(quant_intro,[status(thm)],[908])).
% 0.90/0.86 tff(910,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_24')).
% 0.90/0.86 tff(911,plain,
% 0.90/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[910, 909])).
% 0.90/0.86 tff(912,plain,
% 0.90/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[911, 907])).
% 0.90/0.86 tff(913,plain,
% 0.90/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[912, 905])).
% 0.90/0.86 tff(914,plain,(
% 0.90/0.86 ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.86 inference(skolemize,[status(sab)],[913])).
% 0.90/0.86 tff(915,plain,
% 0.90/0.86 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[914, 904])).
% 0.90/0.86 tff(916,plain,
% 0.90/0.86 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(917,plain,
% 0.90/0.86 ((big_r(f5(c4), f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(918,plain,
% 0.90/0.86 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c4), f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4))))),
% 0.90/0.86 inference(monotonicity,[status(thm)],[917])).
% 0.90/0.87 tff(919,plain,
% 0.90/0.87 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c4), f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4)))),
% 0.90/0.87 inference(transitivity,[status(thm)],[918, 916])).
% 0.90/0.87 tff(920,plain,
% 0.90/0.87 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c4), f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.90/0.87 inference(quant_inst,[status(thm)],[])).
% 0.90/0.87 tff(921,plain,
% 0.90/0.87 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[920, 919])).
% 0.90/0.87 tff(922,plain,
% 0.90/0.87 ((~big_p(c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4))),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[921, 915, 516])).
% 0.90/0.87 tff(923,plain,
% 0.90/0.87 (big_r(f5(c4), f6(c4))),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[922, 860, 517])).
% 0.90/0.87 tff(924,assumption,(big_p(f4(c2))), introduced(assumption)).
% 0.90/0.87 tff(925,assumption,(big_r(f3(c2), f4(c2))), introduced(assumption)).
% 0.90/0.87 tff(926,assumption,(big_r(c2, f3(c2))), introduced(assumption)).
% 0.90/0.87 tff(927,plain,
% 0.90/0.87 ($false),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[650, 196, 926, 925, 924, 923, 902, 881])).
% 0.90/0.87 tff(928,plain,(big_p(f2(c4)) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))) | (~big_p(c3)) | (~big_r(c4, c3))), inference(lemma,lemma(discharge,[]))).
% 0.90/0.87 tff(929,plain,
% 0.90/0.87 (big_p(f2(c4))),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[928, 859, 858, 792, 515, 516])).
% 0.90/0.87 tff(930,plain,
% 0.90/0.87 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl((big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))),
% 0.90/0.87 inference(bind,[status(th)],[])).
% 0.90/0.87 tff(931,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(quant_intro,[status(thm)],[930])).
% 0.90/0.87 tff(932,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(933,plain,
% 0.90/0.87 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ($false | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), rewrite(($false | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))))),
% 0.90/0.87 inference(bind,[status(th)],[])).
% 0.90/0.87 tff(934,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(quant_intro,[status(thm)],[933])).
% 0.90/0.87 tff(935,plain,
% 0.90/0.87 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_p(f6(X1))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))))),
% 0.90/0.87 inference(bind,[status(th)],[])).
% 0.90/0.87 tff(936,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(quant_intro,[status(thm)],[935])).
% 0.90/0.87 tff(937,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_34')).
% 0.90/0.87 tff(938,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[937, 936])).
% 0.90/0.87 tff(939,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[938, 934])).
% 0.90/0.87 tff(940,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[939, 932])).
% 0.90/0.87 tff(941,plain,(
% 0.90/0.87 ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(skolemize,[status(sab)],[940])).
% 0.90/0.87 tff(942,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[941, 931])).
% 0.90/0.87 tff(943,plain,
% 0.90/0.87 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(944,plain,
% 0.90/0.87 ((big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(945,plain,
% 0.90/0.87 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4))))),
% 0.90/0.87 inference(monotonicity,[status(thm)],[944])).
% 0.90/0.87 tff(946,plain,
% 0.90/0.87 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4)))),
% 0.90/0.87 inference(transitivity,[status(thm)],[945, 943])).
% 0.90/0.87 tff(947,plain,
% 0.90/0.87 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.87 inference(quant_inst,[status(thm)],[])).
% 0.90/0.87 tff(948,plain,
% 0.90/0.87 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[947, 946])).
% 0.90/0.87 tff(949,plain,
% 0.90/0.87 ((~big_p(c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4))),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[948, 942, 516])).
% 0.90/0.87 tff(950,plain,
% 0.90/0.87 (big_p(f6(c4))),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[949, 258, 517])).
% 0.90/0.87 tff(951,plain,
% 0.90/0.87 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl((big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))),
% 0.90/0.87 inference(bind,[status(th)],[])).
% 0.90/0.87 tff(952,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(quant_intro,[status(thm)],[951])).
% 0.90/0.87 tff(953,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(954,plain,
% 0.90/0.87 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ($false | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), rewrite(($false | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))))),
% 0.90/0.87 inference(bind,[status(th)],[])).
% 0.90/0.87 tff(955,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(quant_intro,[status(thm)],[954])).
% 0.90/0.87 tff(956,plain,
% 0.90/0.87 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(X1, f5(X1))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))))),
% 0.90/0.87 inference(bind,[status(th)],[])).
% 0.90/0.87 tff(957,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(quant_intro,[status(thm)],[956])).
% 0.90/0.87 tff(958,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_35')).
% 0.90/0.87 tff(959,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[958, 957])).
% 0.90/0.87 tff(960,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[959, 955])).
% 0.90/0.87 tff(961,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[960, 953])).
% 0.90/0.87 tff(962,plain,(
% 0.90/0.87 ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(skolemize,[status(sab)],[961])).
% 0.90/0.87 tff(963,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[962, 952])).
% 0.90/0.87 tff(964,plain,
% 0.90/0.87 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(965,plain,
% 0.90/0.87 ((big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(966,plain,
% 0.90/0.87 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4))))),
% 0.90/0.87 inference(monotonicity,[status(thm)],[965])).
% 0.90/0.87 tff(967,plain,
% 0.90/0.87 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4)))),
% 0.90/0.87 inference(transitivity,[status(thm)],[966, 964])).
% 0.90/0.87 tff(968,plain,
% 0.90/0.87 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.87 inference(quant_inst,[status(thm)],[])).
% 0.90/0.87 tff(969,plain,
% 0.90/0.87 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[968, 967])).
% 0.90/0.87 tff(970,plain,
% 0.90/0.87 ((~big_p(c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4))),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[969, 963, 516])).
% 0.90/0.87 tff(971,plain,
% 0.90/0.87 (big_r(c4, f5(c4))),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[970, 258, 517])).
% 0.90/0.87 tff(972,plain,
% 0.90/0.87 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl((big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))),
% 0.90/0.87 inference(bind,[status(th)],[])).
% 0.90/0.87 tff(973,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(quant_intro,[status(thm)],[972])).
% 0.90/0.87 tff(974,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(975,plain,
% 0.90/0.87 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ($false | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), rewrite(($false | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))))),
% 0.90/0.87 inference(bind,[status(th)],[])).
% 0.90/0.87 tff(976,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(quant_intro,[status(thm)],[975])).
% 0.90/0.87 tff(977,plain,
% 0.90/0.87 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(f5(X1), f6(X1))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))))),
% 0.90/0.87 inference(bind,[status(th)],[])).
% 0.90/0.87 tff(978,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(quant_intro,[status(thm)],[977])).
% 0.90/0.87 tff(979,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_36')).
% 0.90/0.87 tff(980,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[979, 978])).
% 0.90/0.87 tff(981,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[980, 976])).
% 0.90/0.87 tff(982,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[981, 974])).
% 0.90/0.87 tff(983,plain,(
% 0.90/0.87 ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(skolemize,[status(sab)],[982])).
% 0.90/0.87 tff(984,plain,
% 0.90/0.87 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[983, 973])).
% 0.90/0.88 tff(985,plain,
% 0.90/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4)))),
% 0.90/0.88 inference(rewrite,[status(thm)],[])).
% 0.90/0.88 tff(986,plain,
% 0.90/0.88 ((big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4)))),
% 0.90/0.88 inference(rewrite,[status(thm)],[])).
% 0.90/0.88 tff(987,plain,
% 0.90/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4))))),
% 0.90/0.88 inference(monotonicity,[status(thm)],[986])).
% 0.90/0.88 tff(988,plain,
% 0.90/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4)))),
% 0.90/0.88 inference(transitivity,[status(thm)],[987, 985])).
% 0.90/0.88 tff(989,plain,
% 0.90/0.88 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.88 inference(quant_inst,[status(thm)],[])).
% 0.90/0.88 tff(990,plain,
% 0.90/0.88 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[989, 988])).
% 0.90/0.88 tff(991,plain,
% 0.90/0.88 ((~big_p(c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4))),
% 0.90/0.88 inference(unit_resolution,[status(thm)],[990, 984, 516])).
% 0.90/0.88 tff(992,plain,
% 0.90/0.88 (big_r(f5(c4), f6(c4))),
% 0.90/0.88 inference(unit_resolution,[status(thm)],[991, 258, 517])).
% 0.90/0.88 tff(993,plain,
% 0.90/0.88 ($false),
% 0.90/0.88 inference(unit_resolution,[status(thm)],[650, 196, 926, 925, 924, 992, 971, 950])).
% 0.90/0.88 tff(994,plain,(big_r(f1(c4), f2(c4)) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))) | (~big_p(c3)) | (~big_r(c4, c3))), inference(lemma,lemma(discharge,[]))).
% 0.90/0.88 tff(995,plain,
% 0.90/0.88 (big_r(f1(c4), f2(c4))),
% 0.90/0.88 inference(unit_resolution,[status(thm)],[994, 859, 858, 792, 515, 516])).
% 0.90/0.88 tff(996,plain,
% 0.90/0.88 (~big_r(c4, f1(c4))),
% 0.90/0.88 inference(unit_resolution,[status(thm)],[375, 196, 859, 858, 995, 792, 929])).
% 0.90/0.88 tff(997,plain,
% 0.90/0.88 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl((big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.90/0.88 inference(bind,[status(th)],[])).
% 0.90/0.88 tff(998,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(quant_intro,[status(thm)],[997])).
% 0.90/0.88 tff(999,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(rewrite,[status(thm)],[])).
% 0.90/0.88 tff(1000,plain,
% 0.90/0.88 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ($false | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), rewrite(($false | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.90/0.88 inference(bind,[status(th)],[])).
% 0.90/0.88 tff(1001,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(quant_intro,[status(thm)],[1000])).
% 0.90/0.88 tff(1002,plain,
% 0.90/0.88 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.90/0.88 inference(bind,[status(th)],[])).
% 0.90/0.88 tff(1003,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(quant_intro,[status(thm)],[1002])).
% 0.90/0.88 tff(1004,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_28')).
% 0.90/0.88 tff(1005,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 0.90/0.88 tff(1006,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1005, 1001])).
% 0.90/0.88 tff(1007,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1006, 999])).
% 0.90/0.88 tff(1008,plain,(
% 0.90/0.88 ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(skolemize,[status(sab)],[1007])).
% 0.90/0.88 tff(1009,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1008, 998])).
% 0.90/0.88 tff(1010,plain,
% 0.90/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_p(f6(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_p(f6(c4)))),
% 0.90/0.88 inference(rewrite,[status(thm)],[])).
% 0.90/0.88 tff(1011,plain,
% 0.90/0.88 ((big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_p(f6(c4)))),
% 0.90/0.88 inference(rewrite,[status(thm)],[])).
% 0.90/0.88 tff(1012,plain,
% 0.90/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_p(f6(c4))))),
% 0.90/0.88 inference(monotonicity,[status(thm)],[1011])).
% 0.90/0.88 tff(1013,plain,
% 0.90/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_p(f6(c4)))),
% 0.90/0.88 inference(transitivity,[status(thm)],[1012, 1010])).
% 0.90/0.88 tff(1014,plain,
% 0.90/0.88 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.90/0.88 inference(quant_inst,[status(thm)],[])).
% 0.90/0.88 tff(1015,plain,
% 0.90/0.88 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_p(f6(c4))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 0.90/0.88 tff(1016,plain,
% 0.90/0.88 ((~big_p(c3)) | big_r(c4, f1(c4)) | big_p(f6(c4))),
% 0.90/0.88 inference(unit_resolution,[status(thm)],[1015, 1009, 516])).
% 0.90/0.88 tff(1017,plain,
% 0.90/0.88 (big_p(f6(c4))),
% 0.90/0.88 inference(unit_resolution,[status(thm)],[1016, 996, 515])).
% 0.90/0.88 tff(1018,plain,
% 0.90/0.88 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl((big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.90/0.88 inference(bind,[status(th)],[])).
% 0.90/0.88 tff(1019,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(quant_intro,[status(thm)],[1018])).
% 0.90/0.88 tff(1020,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(rewrite,[status(thm)],[])).
% 0.90/0.88 tff(1021,plain,
% 0.90/0.88 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ($false | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), rewrite(($false | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.90/0.88 inference(bind,[status(th)],[])).
% 0.90/0.88 tff(1022,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(quant_intro,[status(thm)],[1021])).
% 0.90/0.88 tff(1023,plain,
% 0.90/0.88 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.90/0.88 inference(bind,[status(th)],[])).
% 0.90/0.88 tff(1024,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(quant_intro,[status(thm)],[1023])).
% 0.90/0.88 tff(1025,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_29')).
% 0.90/0.88 tff(1026,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 0.90/0.88 tff(1027,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1026, 1022])).
% 0.90/0.88 tff(1028,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1027, 1020])).
% 0.90/0.88 tff(1029,plain,(
% 0.90/0.88 ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(skolemize,[status(sab)],[1028])).
% 0.90/0.88 tff(1030,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1029, 1019])).
% 0.90/0.88 tff(1031,plain,
% 0.90/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4)))),
% 0.90/0.88 inference(rewrite,[status(thm)],[])).
% 0.90/0.88 tff(1032,plain,
% 0.90/0.88 ((big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4)))),
% 0.90/0.88 inference(rewrite,[status(thm)],[])).
% 0.90/0.88 tff(1033,plain,
% 0.90/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4))))),
% 0.90/0.88 inference(monotonicity,[status(thm)],[1032])).
% 0.90/0.88 tff(1034,plain,
% 0.90/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4)))),
% 0.90/0.88 inference(transitivity,[status(thm)],[1033, 1031])).
% 0.90/0.88 tff(1035,plain,
% 0.90/0.88 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.90/0.88 inference(quant_inst,[status(thm)],[])).
% 0.90/0.88 tff(1036,plain,
% 0.90/0.88 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 0.90/0.88 tff(1037,plain,
% 0.90/0.88 ((~big_p(c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4))),
% 0.90/0.88 inference(unit_resolution,[status(thm)],[1036, 1030, 516])).
% 0.90/0.88 tff(1038,plain,
% 0.90/0.88 (big_r(c4, f5(c4))),
% 0.90/0.88 inference(unit_resolution,[status(thm)],[1037, 996, 515])).
% 0.90/0.88 tff(1039,plain,
% 0.90/0.88 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl((big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.90/0.88 inference(bind,[status(th)],[])).
% 0.90/0.88 tff(1040,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(quant_intro,[status(thm)],[1039])).
% 0.90/0.88 tff(1041,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(rewrite,[status(thm)],[])).
% 0.90/0.88 tff(1042,plain,
% 0.90/0.88 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ($false | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), rewrite(($false | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.90/0.88 inference(bind,[status(th)],[])).
% 0.90/0.88 tff(1043,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(quant_intro,[status(thm)],[1042])).
% 0.90/0.88 tff(1044,plain,
% 0.90/0.88 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.90/0.88 inference(bind,[status(th)],[])).
% 0.90/0.88 tff(1045,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(quant_intro,[status(thm)],[1044])).
% 0.90/0.88 tff(1046,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_30')).
% 0.90/0.88 tff(1047,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 0.90/0.88 tff(1048,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1047, 1043])).
% 0.90/0.88 tff(1049,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1048, 1041])).
% 0.90/0.88 tff(1050,plain,(
% 0.90/0.88 ![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(skolemize,[status(sab)],[1049])).
% 0.90/0.88 tff(1051,plain,
% 0.90/0.88 (![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1050, 1040])).
% 0.90/0.88 tff(1052,plain,
% 0.90/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4)))),
% 0.90/0.89 inference(rewrite,[status(thm)],[])).
% 0.90/0.89 tff(1053,plain,
% 0.90/0.89 ((big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4)))),
% 0.90/0.89 inference(rewrite,[status(thm)],[])).
% 0.90/0.89 tff(1054,plain,
% 0.90/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4))))),
% 0.90/0.89 inference(monotonicity,[status(thm)],[1053])).
% 0.90/0.89 tff(1055,plain,
% 0.90/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4)))),
% 0.90/0.89 inference(transitivity,[status(thm)],[1054, 1052])).
% 0.90/0.89 tff(1056,plain,
% 0.90/0.89 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.90/0.89 inference(quant_inst,[status(thm)],[])).
% 0.90/0.89 tff(1057,plain,
% 0.90/0.89 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4))),
% 0.90/0.89 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 0.90/0.89 tff(1058,plain,
% 0.90/0.89 ((~big_p(c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[1057, 1051, 516])).
% 0.90/0.89 tff(1059,plain,
% 0.90/0.89 (big_r(f5(c4), f6(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[1058, 996, 515])).
% 0.90/0.89 tff(1060,plain,
% 0.90/0.89 ($false),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[650, 196, 859, 858, 792, 1059, 1038, 1017])).
% 0.90/0.89 tff(1061,plain,(big_p(c2) | (~big_r(c4, c3)) | (~big_p(c4))), inference(lemma,lemma(discharge,[]))).
% 0.90/0.89 tff(1062,plain,
% 0.90/0.89 ($false),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[1061, 470, 4, 430])).
% 0.90/0.89 tff(1063,plain,(big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.89 tff(1064,plain,
% 0.90/0.89 (^[X6: $i, X4: $i, X3: $i, X5: $i] : refl((big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))))),
% 0.90/0.89 inference(bind,[status(th)],[])).
% 0.90/0.89 tff(1065,plain,
% 0.90/0.89 (![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.90/0.89 inference(quant_intro,[status(thm)],[1064])).
% 0.90/0.89 tff(1066,plain,
% 0.90/0.89 (![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.90/0.89 inference(rewrite,[status(thm)],[])).
% 0.90/0.89 tff(1067,plain,
% 0.90/0.89 (^[X6: $i, X4: $i, X3: $i, X5: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(c2)) | big_p(c1)) <=> (big_p(c1) | (~big_p(c2)))), ((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) <=> ((big_p(c1) | (~big_p(c2))) | (~big_p(X3))))), rewrite(((big_p(c1) | (~big_p(c2))) | (~big_p(X3))) <=> (big_p(c1) | (~big_p(X3)) | (~big_p(c2)))), ((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) <=> (big_p(c1) | (~big_p(X3)) | (~big_p(c2))))), (((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) <=> ((big_p(c1) | (~big_p(X3)) | (~big_p(c2))) | (~big_r(c4, X4))))), rewrite(((big_p(c1) | (~big_p(X3)) | (~big_p(c2))) | (~big_r(c4, X4))) <=> (big_p(c1) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4)))), (((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) <=> (big_p(c1) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4))))), ((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> ((big_p(c1) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4))) | (~big_r(X4, X3))))), rewrite(((big_p(c1) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4)))), ((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4))))), (((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) <=> ((big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4))) | (~big_p(X5))))), rewrite(((big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4))) | (~big_p(X5))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X4)))), (((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X4))))), ((((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) <=> ((big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X4))) | (~big_r(c4, X6))))), rewrite(((big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X4))) | (~big_r(c4, X6))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))), ((((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))))), (((((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> ((big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) | (~big_r(X6, X5))))), rewrite(((big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) | (~big_r(X6, X5))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))), (((((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))))),
% 0.90/0.89 inference(bind,[status(th)],[])).
% 0.90/0.89 tff(1068,plain,
% 0.90/0.89 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.90/0.89 inference(quant_intro,[status(thm)],[1067])).
% 0.90/0.89 tff(1069,axiom,(![X6: $i, X4: $i, X3: $i, X5: $i] : ((((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_60')).
% 0.90/0.89 tff(1070,plain,
% 0.90/0.89 (![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.90/0.89 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 0.90/0.89 tff(1071,plain,
% 0.90/0.89 (![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.90/0.89 inference(modus_ponens,[status(thm)],[1070, 1066])).
% 0.90/0.89 tff(1072,plain,(
% 0.90/0.89 ![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.90/0.89 inference(skolemize,[status(sab)],[1071])).
% 0.90/0.89 tff(1073,plain,
% 0.90/0.89 (![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.90/0.89 inference(modus_ponens,[status(thm)],[1072, 1065])).
% 0.90/0.89 tff(1074,plain,
% 0.90/0.89 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_p(c2)) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.90/0.89 inference(rewrite,[status(thm)],[])).
% 0.90/0.89 tff(1075,plain,
% 0.90/0.89 ((big_p(c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4)))) <=> (big_p(c1) | (~big_p(c2)) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.90/0.89 inference(rewrite,[status(thm)],[])).
% 0.90/0.89 tff(1076,plain,
% 0.90/0.89 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_p(c2)) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4)))))),
% 0.90/0.89 inference(monotonicity,[status(thm)],[1075])).
% 0.90/0.89 tff(1077,plain,
% 0.90/0.89 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.90/0.89 inference(transitivity,[status(thm)],[1076, 1074])).
% 0.90/0.89 tff(1078,plain,
% 0.90/0.89 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4))))),
% 0.90/0.89 inference(quant_inst,[status(thm)],[])).
% 0.90/0.89 tff(1079,plain,
% 0.90/0.89 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4)))),
% 0.90/0.89 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 0.90/0.89 tff(1080,plain,
% 0.90/0.89 (~big_p(f4(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[1079, 2, 1063, 1073, 77, 98])).
% 0.90/0.89 tff(1081,plain,
% 0.90/0.89 ($false),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[348, 48, 5, 3, 1080])).
% 0.90/0.89 tff(1082,plain,(big_r(c4, f1(c4)) | big_p(c4) | big_p(c1)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.89 tff(1083,plain,
% 0.90/0.89 (big_r(c4, f1(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[1082, 2, 5])).
% 0.90/0.89 tff(1084,plain,
% 0.90/0.89 (big_r(f1(c4), f2(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[292, 361])).
% 0.90/0.89 tff(1085,plain,
% 0.90/0.89 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.90/0.89 inference(rewrite,[status(thm)],[])).
% 0.90/0.89 tff(1086,plain,
% 0.90/0.89 ((big_p(c1) | (~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4)))) <=> (big_p(c1) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.90/0.89 inference(rewrite,[status(thm)],[])).
% 0.90/0.89 tff(1087,plain,
% 0.90/0.89 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4)))))),
% 0.90/0.89 inference(monotonicity,[status(thm)],[1086])).
% 0.90/0.89 tff(1088,plain,
% 0.90/0.89 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.90/0.89 inference(transitivity,[status(thm)],[1087, 1085])).
% 0.90/0.89 tff(1089,plain,
% 0.90/0.89 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4))))),
% 0.90/0.89 inference(quant_inst,[status(thm)],[])).
% 0.90/0.89 tff(1090,plain,
% 0.90/0.89 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4)))),
% 0.90/0.89 inference(modus_ponens,[status(thm)],[1089, 1088])).
% 0.90/0.89 tff(1091,plain,
% 0.90/0.89 (~big_p(f2(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[1090, 2, 1063, 1073, 1084, 1083])).
% 0.90/0.89 tff(1092,plain,
% 0.90/0.89 ($false),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[367, 112, 5, 361, 1091])).
% 0.90/0.89 tff(1093,plain,(big_r(c4, f3(c4)) | big_p(c4) | big_p(c1)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.89 tff(1094,plain,
% 0.90/0.89 (big_r(c4, f3(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[1093, 2, 5])).
% 0.90/0.89 tff(1095,plain,
% 0.90/0.89 (~big_p(f4(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[1079, 2, 1063, 1073, 1094, 314])).
% 0.90/0.89 tff(1096,plain,
% 0.90/0.89 ($false),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[277, 271, 5, 258, 1095])).
% 0.90/0.89 tff(1097,plain,(big_r(f1(c4), f2(c4)) | big_p(c4) | big_p(c1)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.89 tff(1098,plain,
% 0.90/0.89 (big_r(f1(c4), f2(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[1097, 2, 5])).
% 0.90/0.89 tff(1099,plain,
% 0.90/0.89 (~big_p(f2(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[1090, 2, 1063, 1073, 1098, 1083])).
% 0.90/0.89 tff(1100,plain,
% 0.90/0.89 (big_r(f3(c4), f4(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[418, 244, 5, 1099])).
% 0.90/0.89 tff(1101,plain,
% 0.90/0.89 (~big_p(f4(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[1079, 2, 1063, 1073, 1094, 1100])).
% 0.90/0.89 tff(1102,plain,
% 0.90/0.89 ($false),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[427, 19, 5, 1101, 1099])).
% 0.90/0.89 tff(1103,plain,(big_p(c1) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.89 tff(1104,plain,
% 0.90/0.89 (big_p(c1)),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[1103, 5])).
% 0.90/0.89 tff(1105,assumption,(~big_r(c2, c1)), introduced(assumption)).
% 0.90/0.89 tff(1106,plain,
% 0.90/0.89 (big_p(c2)),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[429, 5])).
% 0.90/0.89 tff(1107,plain,
% 0.90/0.89 (big_r(c4, f1(c4)) | big_p(f4(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[348, 48, 5])).
% 0.90/0.89 tff(1108,plain,
% 0.90/0.89 (big_p(f4(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[1107, 3])).
% 0.90/0.89 tff(1109,assumption,(big_p(c2)), introduced(assumption)).
% 0.90/0.89 tff(1110,assumption,(~big_r(f3(c4), f4(c4))), introduced(assumption)).
% 0.90/0.89 tff(1111,plain,
% 0.90/0.89 (big_r(c4, f1(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[97, 1110])).
% 0.90/0.89 tff(1112,plain,
% 0.90/0.89 (big_r(f1(c4), f2(c4))),
% 0.90/0.89 inference(unit_resolution,[status(thm)],[313, 1110])).
% 0.90/0.89 tff(1113,plain,
% 0.90/0.89 (^[X6: $i, X4: $i, X3: $i, X5: $i] : refl(((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))))),
% 0.90/0.89 inference(bind,[status(th)],[])).
% 0.90/0.89 tff(1114,plain,
% 0.90/0.89 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.90/0.89 inference(quant_intro,[status(thm)],[1113])).
% 0.90/0.89 tff(1115,plain,
% 0.90/0.89 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.90/0.89 inference(rewrite,[status(thm)],[])).
% 0.90/0.89 tff(1116,plain,
% 0.90/0.89 (^[X6: $i, X4: $i, X3: $i, X5: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) <=> ((~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1))), (((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) <=> (((~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1)) | (~big_r(c4, X4))))), rewrite((((~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1)) | (~big_r(c4, X4))) <=> ((~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4)))), (((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) <=> ((~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4))))), ((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> (((~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4))) | (~big_r(X4, X3))))), rewrite((((~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4)))), ((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4))))), (((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) <=> (((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4))) | (~big_p(X5))))), rewrite((((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4))) | (~big_p(X5))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X4)))), (((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X4))))), ((((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) <=> (((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X4))) | (~big_r(c4, X6))))), rewrite((((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X4))) | (~big_r(c4, X6))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X6)) | (~big_r(c4, X4)))), ((((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X6)) | (~big_r(c4, X4))))), (((((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> (((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X6)) | (~big_r(c4, X4))) | (~big_r(X6, X5))))), rewrite((((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X6)) | (~big_r(c4, X4))) | (~big_r(X6, X5))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))), (((((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))))),
% 0.90/0.89 inference(bind,[status(th)],[])).
% 0.90/0.89 tff(1117,plain,
% 0.90/0.89 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.90/0.89 inference(quant_intro,[status(thm)],[1116])).
% 0.90/0.89 tff(1118,axiom,(![X6: $i, X4: $i, X3: $i, X5: $i] : ((((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_72')).
% 0.90/0.89 tff(1119,plain,
% 0.90/0.89 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.90/0.89 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 0.90/0.89 tff(1120,plain,
% 0.90/0.89 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.90/0.89 inference(modus_ponens,[status(thm)],[1119, 1115])).
% 0.90/0.89 tff(1121,plain,(
% 0.90/0.89 ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.90/0.89 inference(skolemize,[status(sab)],[1120])).
% 0.90/0.90 tff(1122,plain,
% 0.90/0.90 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1121, 1114])).
% 0.90/0.90 tff(1123,plain,
% 0.90/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_p(c2)) | big_r(c2, c1) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1124,plain,
% 0.90/0.90 (((~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | big_r(c2, c1) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4)))) <=> ((~big_p(c2)) | big_r(c2, c1) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1125,plain,
% 0.90/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | big_r(c2, c1) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_p(c2)) | big_r(c2, c1) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4)))))),
% 0.90/0.90 inference(monotonicity,[status(thm)],[1124])).
% 0.90/0.90 tff(1126,plain,
% 0.90/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | big_r(c2, c1) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.90/0.90 inference(transitivity,[status(thm)],[1125, 1123])).
% 0.90/0.90 tff(1127,plain,
% 0.90/0.90 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | big_r(c2, c1) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4))))),
% 0.90/0.90 inference(quant_inst,[status(thm)],[])).
% 0.90/0.90 tff(1128,plain,
% 0.90/0.90 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4)))),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 0.90/0.90 tff(1129,plain,
% 0.90/0.90 (~big_p(f2(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1128, 1109, 1105, 1122, 1112, 1111])).
% 0.90/0.90 tff(1130,plain,
% 0.90/0.90 ($false),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[418, 244, 5, 1110, 1129])).
% 0.90/0.90 tff(1131,plain,(big_r(f3(c4), f4(c4)) | big_p(c4) | (~big_p(c2)) | big_r(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.90 tff(1132,plain,
% 0.90/0.90 (big_r(f3(c4), f4(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1131, 5, 1109, 1105])).
% 0.90/0.90 tff(1133,plain,
% 0.90/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_p(c2)) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1134,plain,
% 0.90/0.90 (((~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4)))) <=> ((~big_p(c2)) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1135,plain,
% 0.90/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_p(c2)) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4)))))),
% 0.90/0.90 inference(monotonicity,[status(thm)],[1134])).
% 0.90/0.90 tff(1136,plain,
% 0.90/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.90/0.90 inference(transitivity,[status(thm)],[1135, 1133])).
% 0.90/0.90 tff(1137,plain,
% 0.90/0.90 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4))))),
% 0.90/0.90 inference(quant_inst,[status(thm)],[])).
% 0.90/0.90 tff(1138,plain,
% 0.90/0.90 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4)))),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 0.90/0.90 tff(1139,plain,
% 0.90/0.90 ((~big_p(f4(c4))) | (~big_r(c4, f3(c4)))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1138, 1109, 1105, 1122, 1132])).
% 0.90/0.90 tff(1140,plain,
% 0.90/0.90 ($false),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1139, 1108, 77])).
% 0.90/0.90 tff(1141,plain,(big_r(c4, f1(c4)) | (~big_p(c2)) | big_r(c2, c1) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.90 tff(1142,plain,
% 0.90/0.90 (big_r(c4, f1(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1141, 5, 1105, 1106])).
% 0.90/0.90 tff(1143,plain,
% 0.90/0.90 (big_r(c4, f1(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1141, 1109, 1105, 5])).
% 0.90/0.90 tff(1144,assumption,(~big_p(f4(c4))), introduced(assumption)).
% 0.90/0.90 tff(1145,plain,
% 0.90/0.90 (big_r(f1(c4), f2(c4)) | big_p(f4(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[277, 271, 5])).
% 0.90/0.90 tff(1146,plain,
% 0.90/0.90 (big_r(f1(c4), f2(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1145, 1144])).
% 0.90/0.90 tff(1147,plain,
% 0.90/0.90 (~big_p(f2(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1128, 1109, 1105, 1122, 1146, 1143])).
% 0.90/0.90 tff(1148,plain,
% 0.90/0.90 ($false),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[427, 19, 5, 1144, 1147])).
% 0.90/0.90 tff(1149,plain,(big_p(f4(c4)) | big_p(c4) | (~big_p(c2)) | big_r(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.90 tff(1150,plain,
% 0.90/0.90 (big_p(f4(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1149, 1106, 5, 1105])).
% 0.90/0.90 tff(1151,plain,
% 0.90/0.90 (big_r(f3(c4), f4(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1131, 1106, 5, 1105])).
% 0.90/0.90 tff(1152,plain,
% 0.90/0.90 (~big_r(c4, f3(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1138, 1106, 1105, 1122, 1151, 1150])).
% 0.90/0.90 tff(1153,plain,
% 0.90/0.90 (big_r(f1(c4), f2(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[292, 1152])).
% 0.90/0.90 tff(1154,plain,
% 0.90/0.90 (~big_p(f2(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1128, 1106, 1105, 1122, 1153, 1142])).
% 0.90/0.90 tff(1155,plain,
% 0.90/0.90 ($false),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[367, 112, 5, 1152, 1154])).
% 0.90/0.90 tff(1156,plain,(big_p(c4) | big_r(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.90 tff(1157,plain,
% 0.90/0.90 (big_p(c4)),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1156, 1105])).
% 0.90/0.90 tff(1158,plain,
% 0.90/0.90 (big_p(c2)),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[469, 431])).
% 0.90/0.90 tff(1159,plain,
% 0.90/0.90 (((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)) <=> ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1160,plain,
% 0.90/0.90 ((((~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)) | big_r(c4, c3)) <=> ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1161,plain,
% 0.90/0.90 ((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(c4))) <=> ((~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1162,plain,
% 0.90/0.90 (((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(c4))) | big_r(c4, c3)) <=> (((~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)) | big_r(c4, c3))),
% 0.90/0.90 inference(monotonicity,[status(thm)],[1161])).
% 0.90/0.90 tff(1163,plain,
% 0.90/0.90 (((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(c4))) | big_r(c4, c3)) <=> ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1))),
% 0.90/0.90 inference(transitivity,[status(thm)],[1162, 1160])).
% 0.90/0.90 tff(1164,axiom,((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(c4))) | big_r(c4, c3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_67')).
% 0.90/0.90 tff(1165,plain,
% 0.90/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 0.90/0.90 tff(1166,plain,
% 0.90/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1165, 1159])).
% 0.90/0.90 tff(1167,plain,
% 0.90/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1166, 1159])).
% 0.90/0.90 tff(1168,plain,
% 0.90/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1167, 1159])).
% 0.90/0.90 tff(1169,plain,
% 0.90/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1168, 1159])).
% 0.90/0.90 tff(1170,plain,
% 0.90/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1169, 1159])).
% 0.90/0.90 tff(1171,plain,
% 0.90/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1170, 1159])).
% 0.90/0.90 tff(1172,plain,
% 0.90/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1171, 1159])).
% 0.90/0.90 tff(1173,plain,
% 0.90/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1172, 1159])).
% 0.90/0.90 tff(1174,plain,
% 0.90/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1173, 1159])).
% 0.90/0.90 tff(1175,plain,
% 0.90/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1174, 1159])).
% 0.90/0.90 tff(1176,plain,
% 0.90/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1175, 1159])).
% 0.90/0.90 tff(1177,plain,
% 0.90/0.90 (~big_p(c4)),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1176, 1158, 431, 1105])).
% 0.90/0.90 tff(1178,plain,
% 0.90/0.90 (big_r(c4, f1(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1141, 1158, 1105, 1177])).
% 0.90/0.90 tff(1179,plain,
% 0.90/0.90 (big_p(f4(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1149, 1177, 1158, 1105])).
% 0.90/0.90 tff(1180,plain,
% 0.90/0.90 (big_r(f3(c4), f4(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1131, 1177, 1158, 1105])).
% 0.90/0.90 tff(1181,plain,
% 0.90/0.90 ((~big_p(f4(c4))) | (~big_r(c4, f3(c4)))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1138, 1158, 1105, 1122, 1180])).
% 0.90/0.90 tff(1182,plain,
% 0.90/0.90 (~big_r(c4, f3(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1181, 1179])).
% 0.90/0.90 tff(1183,plain,
% 0.90/0.90 (big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[291, 144, 1177])).
% 0.90/0.90 tff(1184,plain,
% 0.90/0.90 (big_r(f1(c4), f2(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1183, 1182])).
% 0.90/0.90 tff(1185,plain,
% 0.90/0.90 (~big_p(f2(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1128, 1158, 1105, 1122, 1184, 1178])).
% 0.90/0.90 tff(1186,plain,
% 0.90/0.90 ($false),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[367, 112, 1177, 1182, 1185])).
% 0.90/0.90 tff(1187,plain,(big_r(c4, c3) | big_r(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.90 tff(1188,plain,
% 0.90/0.90 (big_r(c4, c3)),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1187, 1105])).
% 0.90/0.90 tff(1189,plain,
% 0.90/0.90 (big_p(c2)),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1061, 1188, 1157])).
% 0.90/0.90 tff(1190,plain,
% 0.90/0.90 ((big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)) <=> (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1191,plain,
% 0.90/0.90 ((((~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)) | big_p(c3)) <=> (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1192,plain,
% 0.90/0.90 (((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(c4))) | big_p(c3)) <=> (((~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)) | big_p(c3))),
% 0.90/0.90 inference(monotonicity,[status(thm)],[1161])).
% 0.90/0.90 tff(1193,plain,
% 0.90/0.90 (((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(c4))) | big_p(c3)) <=> (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1))),
% 0.90/0.90 inference(transitivity,[status(thm)],[1192, 1191])).
% 0.90/0.90 tff(1194,axiom,((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(c4))) | big_p(c3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_66')).
% 0.90/0.90 tff(1195,plain,
% 0.90/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1194, 1193])).
% 0.90/0.90 tff(1196,plain,
% 0.90/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1195, 1190])).
% 0.90/0.90 tff(1197,plain,
% 0.90/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1196, 1190])).
% 0.90/0.90 tff(1198,plain,
% 0.90/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1197, 1190])).
% 0.90/0.90 tff(1199,plain,
% 0.90/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1198, 1190])).
% 0.90/0.90 tff(1200,plain,
% 0.90/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1199, 1190])).
% 0.90/0.90 tff(1201,plain,
% 0.90/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1200, 1190])).
% 0.90/0.90 tff(1202,plain,
% 0.90/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1201, 1190])).
% 0.90/0.90 tff(1203,plain,
% 0.90/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1202, 1190])).
% 0.90/0.90 tff(1204,plain,
% 0.90/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1203, 1190])).
% 0.90/0.90 tff(1205,plain,
% 0.90/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1204, 1190])).
% 0.90/0.90 tff(1206,plain,
% 0.90/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1205, 1190])).
% 0.90/0.90 tff(1207,plain,
% 0.90/0.90 (big_p(c3)),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1206, 1189, 1157, 1105])).
% 0.90/0.90 tff(1208,plain,
% 0.90/0.90 ((~big_p(c3)) | big_p(f6(c4)) | big_p(f2(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[879, 873, 1188])).
% 0.90/0.90 tff(1209,plain,
% 0.90/0.90 (big_p(f6(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1208, 860, 1207])).
% 0.90/0.90 tff(1210,plain,
% 0.90/0.90 ((~big_p(c3)) | big_r(c4, f5(c4)) | big_p(f2(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[900, 894, 1188])).
% 0.90/0.90 tff(1211,plain,
% 0.90/0.90 (big_r(c4, f5(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1210, 860, 1207])).
% 0.90/0.90 tff(1212,plain,
% 0.90/0.90 ((~big_p(c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[921, 915, 1188])).
% 0.90/0.90 tff(1213,plain,
% 0.90/0.90 (big_r(f5(c4), f6(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1212, 860, 1207])).
% 0.90/0.90 tff(1214,plain,
% 0.90/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_p(c2)) | big_r(c2, c1) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1215,plain,
% 0.90/0.90 (((~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | big_r(c2, c1) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4)))) <=> ((~big_p(c2)) | big_r(c2, c1) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1216,plain,
% 0.90/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | big_r(c2, c1) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_p(c2)) | big_r(c2, c1) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4)))))),
% 0.90/0.90 inference(monotonicity,[status(thm)],[1215])).
% 0.90/0.90 tff(1217,plain,
% 0.90/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | big_r(c2, c1) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.90/0.90 inference(transitivity,[status(thm)],[1216, 1214])).
% 0.90/0.90 tff(1218,plain,
% 0.90/0.90 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | big_r(c2, c1) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4))))),
% 0.90/0.90 inference(quant_inst,[status(thm)],[])).
% 0.90/0.90 tff(1219,plain,
% 0.90/0.90 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4)))),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 0.90/0.90 tff(1220,plain,
% 0.90/0.90 ($false),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1219, 1189, 1105, 1122, 1213, 1211, 1209])).
% 0.90/0.90 tff(1221,plain,(big_p(f2(c4)) | big_r(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.90 tff(1222,plain,
% 0.90/0.90 (big_p(f2(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1221, 1105])).
% 0.90/0.90 tff(1223,assumption,(~big_p(f6(c4))), introduced(assumption)).
% 0.90/0.90 tff(1224,plain,
% 0.90/0.90 ((~big_p(c3)) | big_r(c4, f1(c4)) | big_p(f6(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1015, 1009, 1188])).
% 0.90/0.90 tff(1225,plain,
% 0.90/0.90 (big_r(c4, f1(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1224, 1223, 1207])).
% 0.90/0.90 tff(1226,plain,
% 0.90/0.90 ((~big_p(c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[948, 942, 1188])).
% 0.90/0.90 tff(1227,plain,
% 0.90/0.90 (big_r(f1(c4), f2(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1226, 1223, 1207])).
% 0.90/0.90 tff(1228,plain,
% 0.90/0.90 ($false),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1128, 1189, 1105, 1122, 1227, 1225, 1222])).
% 0.90/0.90 tff(1229,plain,(big_p(f6(c4)) | big_r(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.90 tff(1230,plain,
% 0.90/0.90 (big_p(f6(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1229, 1105])).
% 0.90/0.90 tff(1231,plain,
% 0.90/0.90 ((~big_p(c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[969, 963, 1188])).
% 0.90/0.90 tff(1232,plain,
% 0.90/0.90 (big_r(c4, f5(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1231, 258, 1207])).
% 0.90/0.90 tff(1233,plain,
% 0.90/0.90 ((~big_p(c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[990, 984, 1188])).
% 0.90/0.90 tff(1234,plain,
% 0.90/0.90 (big_r(f5(c4), f6(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1233, 258, 1207])).
% 0.90/0.90 tff(1235,plain,
% 0.90/0.90 ($false),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1219, 1189, 1105, 1122, 1234, 1232, 1230])).
% 0.90/0.90 tff(1236,plain,(big_r(f1(c4), f2(c4)) | big_r(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.90 tff(1237,plain,
% 0.90/0.90 (big_r(f1(c4), f2(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1236, 1105])).
% 0.90/0.90 tff(1238,plain,
% 0.90/0.90 (~big_r(c4, f1(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1128, 1189, 1105, 1122, 1237, 1222])).
% 0.90/0.90 tff(1239,plain,
% 0.90/0.90 ((~big_p(c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1036, 1030, 1188])).
% 0.90/0.90 tff(1240,plain,
% 0.90/0.90 (big_r(c4, f5(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1239, 1238, 1207])).
% 0.90/0.90 tff(1241,plain,
% 0.90/0.90 ((~big_p(c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1057, 1051, 1188])).
% 0.90/0.90 tff(1242,plain,
% 0.90/0.90 (big_r(f5(c4), f6(c4))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1241, 1238, 1207])).
% 0.90/0.90 tff(1243,plain,
% 0.90/0.90 ($false),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1219, 1189, 1105, 1122, 1242, 1240, 1230])).
% 0.90/0.90 tff(1244,plain,(big_r(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.90 tff(1245,plain,
% 0.90/0.90 (^[X2: $i, X7: $i, X1: $i] : refl((big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.90/0.90 inference(bind,[status(th)],[])).
% 0.90/0.90 tff(1246,plain,
% 0.90/0.90 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.90 inference(quant_intro,[status(thm)],[1245])).
% 0.90/0.90 tff(1247,plain,
% 0.90/0.90 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1248,plain,
% 0.90/0.90 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ($false | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))))), rewrite(($false | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.90/0.91 inference(bind,[status(th)],[])).
% 0.90/0.91 tff(1249,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.91 inference(quant_intro,[status(thm)],[1248])).
% 0.90/0.91 tff(1250,plain,
% 0.90/0.91 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_p(f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))))), ((((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.90/0.91 inference(bind,[status(th)],[])).
% 0.90/0.91 tff(1251,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.91 inference(quant_intro,[status(thm)],[1250])).
% 0.90/0.91 tff(1252,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_4')).
% 0.90/0.91 tff(1253,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 0.90/0.91 tff(1254,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1253, 1249])).
% 0.90/0.91 tff(1255,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1254, 1247])).
% 0.90/0.91 tff(1256,plain,(
% 0.90/0.91 ![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.91 inference(skolemize,[status(sab)],[1255])).
% 0.90/0.91 tff(1257,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1256, 1246])).
% 0.90/0.91 tff(1258,plain,
% 0.90/0.91 (((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1259,plain,
% 0.90/0.91 ((big_p(f2(c4)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> (big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1260,plain,
% 0.90/0.91 (((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f2(c4)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_p(f2(c4))))),
% 0.90/0.91 inference(monotonicity,[status(thm)],[1259])).
% 0.90/0.91 tff(1261,plain,
% 0.90/0.91 (((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f2(c4)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 0.90/0.91 inference(transitivity,[status(thm)],[1260, 1258])).
% 0.90/0.91 tff(1262,plain,
% 0.90/0.91 ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f2(c4)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.90/0.91 inference(quant_inst,[status(thm)],[])).
% 0.90/0.91 tff(1263,plain,
% 0.90/0.91 ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_p(f2(c4))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 0.90/0.91 tff(1264,plain,
% 0.90/0.91 (big_p(f6(c2)) | big_p(f2(c4))),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1263, 1257, 1104, 5, 1244])).
% 0.90/0.91 tff(1265,plain,
% 0.90/0.91 (big_p(f6(c2))),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1264, 860])).
% 0.90/0.91 tff(1266,plain,
% 0.90/0.91 (^[X2: $i, X7: $i, X1: $i] : refl((big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))))),
% 0.90/0.91 inference(bind,[status(th)],[])).
% 0.90/0.91 tff(1267,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.90/0.91 inference(quant_intro,[status(thm)],[1266])).
% 0.90/0.91 tff(1268,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1269,plain,
% 0.90/0.91 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> ($false | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))))), rewrite(($false | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))), (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))))),
% 0.90/0.91 inference(bind,[status(th)],[])).
% 0.90/0.91 tff(1270,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.90/0.91 inference(quant_intro,[status(thm)],[1269])).
% 0.90/0.91 tff(1271,plain,
% 0.90/0.91 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_p(f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))))), ((((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))), ((((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))))),
% 0.90/0.91 inference(bind,[status(th)],[])).
% 0.90/0.91 tff(1272,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.90/0.91 inference(quant_intro,[status(thm)],[1271])).
% 0.90/0.91 tff(1273,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5')).
% 0.90/0.91 tff(1274,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 0.90/0.91 tff(1275,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1274, 1270])).
% 0.90/0.91 tff(1276,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1275, 1268])).
% 0.90/0.91 tff(1277,plain,(
% 0.90/0.91 ![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.90/0.91 inference(skolemize,[status(sab)],[1276])).
% 0.90/0.91 tff(1278,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1277, 1267])).
% 0.90/0.91 tff(1279,plain,
% 0.90/0.91 (((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1280,plain,
% 0.90/0.91 ((big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2))) <=> (big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1281,plain,
% 0.90/0.91 (((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_p(f2(c4))))),
% 0.90/0.91 inference(monotonicity,[status(thm)],[1280])).
% 0.90/0.91 tff(1282,plain,
% 0.90/0.91 (((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 0.90/0.91 inference(transitivity,[status(thm)],[1281, 1279])).
% 0.90/0.91 tff(1283,plain,
% 0.90/0.91 ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)))),
% 0.90/0.91 inference(quant_inst,[status(thm)],[])).
% 0.90/0.91 tff(1284,plain,
% 0.90/0.91 ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_p(f2(c4))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 0.90/0.91 tff(1285,plain,
% 0.90/0.91 (big_r(c2, f5(c2)) | big_p(f2(c4))),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1284, 1278, 1104, 5, 1244])).
% 0.90/0.91 tff(1286,plain,
% 0.90/0.91 (big_r(c2, f5(c2))),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1285, 860])).
% 0.90/0.91 tff(1287,plain,
% 0.90/0.91 (^[X2: $i, X7: $i, X1: $i] : refl((big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))))),
% 0.90/0.91 inference(bind,[status(th)],[])).
% 0.90/0.91 tff(1288,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.90/0.91 inference(quant_intro,[status(thm)],[1287])).
% 0.90/0.91 tff(1289,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1290,plain,
% 0.90/0.91 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(mp(asserted((big_p(a) | big_p(a)) | big_p(a)), trans(monotonicity(rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a)))), rewrite((big_p(a) | big_p(a)) <=> big_p(a)), (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a))), big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> ($false | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))))), rewrite(($false | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))), (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))))),
% 0.90/0.91 inference(bind,[status(th)],[])).
% 0.90/0.91 tff(1291,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.90/0.91 inference(quant_intro,[status(thm)],[1290])).
% 0.90/0.91 tff(1292,plain,
% 0.90/0.91 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_p(f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))))), ((((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))), ((((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))))),
% 0.90/0.91 inference(bind,[status(th)],[])).
% 0.90/0.91 tff(1293,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.90/0.91 inference(quant_intro,[status(thm)],[1292])).
% 0.90/0.91 tff(1294,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6')).
% 0.90/0.91 tff(1295,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1294, 1293])).
% 0.90/0.91 tff(1296,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1295, 1291])).
% 0.90/0.91 tff(1297,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1296, 1289])).
% 0.90/0.91 tff(1298,plain,(
% 0.90/0.91 ![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.90/0.91 inference(skolemize,[status(sab)],[1297])).
% 0.90/0.91 tff(1299,plain,
% 0.90/0.91 (![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1298, 1288])).
% 0.90/0.91 tff(1300,plain,
% 0.90/0.91 (((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1301,plain,
% 0.90/0.91 ((big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2))) <=> (big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1302,plain,
% 0.90/0.91 (((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_p(f2(c4))))),
% 0.90/0.91 inference(monotonicity,[status(thm)],[1301])).
% 0.90/0.91 tff(1303,plain,
% 0.90/0.91 (((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 0.90/0.91 inference(transitivity,[status(thm)],[1302, 1300])).
% 0.90/0.91 tff(1304,plain,
% 0.90/0.91 ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)))),
% 0.90/0.91 inference(quant_inst,[status(thm)],[])).
% 0.90/0.91 tff(1305,plain,
% 0.90/0.91 ((~![X2: $i, X7: $i, X1: $i] : (big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_p(f2(c4))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 0.90/0.91 tff(1306,plain,
% 0.90/0.91 (big_r(f5(c2), f6(c2)) | big_p(f2(c4))),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1305, 1299, 1104, 5, 1244])).
% 0.90/0.91 tff(1307,plain,
% 0.90/0.91 (big_r(f5(c2), f6(c2))),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1306, 860])).
% 0.90/0.91 tff(1308,plain,
% 0.90/0.91 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_p(f4(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_p(f4(c4)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1309,plain,
% 0.90/0.91 ((big_p(f4(c4)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> (big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_p(f4(c4)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1310,plain,
% 0.90/0.91 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(f4(c4)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_p(f4(c4))))),
% 0.90/0.91 inference(monotonicity,[status(thm)],[1309])).
% 0.90/0.91 tff(1311,plain,
% 0.90/0.91 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(f4(c4)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_p(f4(c4)))),
% 0.90/0.91 inference(transitivity,[status(thm)],[1310, 1308])).
% 0.90/0.91 tff(1312,plain,
% 0.90/0.91 ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(f4(c4)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.90/0.91 inference(quant_inst,[status(thm)],[])).
% 0.90/0.91 tff(1313,plain,
% 0.90/0.91 ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_p(f4(c4))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1312, 1311])).
% 0.90/0.91 tff(1314,plain,
% 0.90/0.91 (big_p(f2(c2)) | big_p(f4(c4))),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1313, 530, 1104, 5, 1244])).
% 0.90/0.91 tff(1315,plain,
% 0.90/0.91 (big_p(f2(c2))),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1314, 1144])).
% 0.90/0.91 tff(1316,plain,
% 0.90/0.91 (big_p(f4(c4)) | big_p(f2(c4))),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[427, 19, 5])).
% 0.90/0.91 tff(1317,plain,
% 0.90/0.91 (big_p(f2(c4))),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1316, 1144])).
% 0.90/0.91 tff(1318,plain,
% 0.90/0.91 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1319,plain,
% 0.90/0.91 ((big_p(c4) | big_r(c4, f1(c4)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> (big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1320,plain,
% 0.90/0.91 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(c4) | big_r(c4, f1(c4)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4))))),
% 0.90/0.91 inference(monotonicity,[status(thm)],[1319])).
% 0.90/0.91 tff(1321,plain,
% 0.90/0.91 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(c4) | big_r(c4, f1(c4)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 0.90/0.91 inference(transitivity,[status(thm)],[1320, 1318])).
% 0.90/0.91 tff(1322,plain,
% 0.90/0.91 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(c4) | big_r(c4, f1(c4)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.90/0.92 inference(quant_inst,[status(thm)],[])).
% 0.90/0.92 tff(1323,plain,
% 0.90/0.92 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4))),
% 0.90/0.92 inference(modus_ponens,[status(thm)],[1322, 1321])).
% 0.90/0.92 tff(1324,plain,
% 0.90/0.92 ((~big_p(c1)) | big_p(f6(c2)) | big_r(c4, f1(c4))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1323, 667, 5, 1244])).
% 0.90/0.92 tff(1325,plain,
% 0.90/0.92 (big_p(f6(c2))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1324, 3, 1104])).
% 0.90/0.92 tff(1326,plain,
% 0.90/0.92 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(1327,plain,
% 0.90/0.92 ((big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2))) <=> (big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(1328,plain,
% 0.90/0.92 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4))))),
% 0.90/0.92 inference(monotonicity,[status(thm)],[1327])).
% 0.90/0.92 tff(1329,plain,
% 0.90/0.92 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 0.90/0.92 inference(transitivity,[status(thm)],[1328, 1326])).
% 0.90/0.92 tff(1330,plain,
% 0.90/0.92 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)))),
% 0.90/0.92 inference(quant_inst,[status(thm)],[])).
% 0.90/0.92 tff(1331,plain,
% 0.90/0.92 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4))),
% 0.90/0.92 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 0.90/0.92 tff(1332,plain,
% 0.90/0.92 ((~big_p(c1)) | big_r(c2, f5(c2)) | big_r(c4, f1(c4))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1331, 688, 5, 1244])).
% 0.90/0.92 tff(1333,plain,
% 0.90/0.92 (big_r(c2, f5(c2))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1332, 3, 1104])).
% 0.90/0.92 tff(1334,plain,
% 0.90/0.92 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(1335,plain,
% 0.90/0.92 ((big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2))) <=> (big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(1336,plain,
% 0.90/0.92 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4))))),
% 0.90/0.92 inference(monotonicity,[status(thm)],[1335])).
% 0.90/0.92 tff(1337,plain,
% 0.90/0.92 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 0.90/0.92 inference(transitivity,[status(thm)],[1336, 1334])).
% 0.90/0.92 tff(1338,plain,
% 0.90/0.92 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)))),
% 0.90/0.92 inference(quant_inst,[status(thm)],[])).
% 0.90/0.92 tff(1339,plain,
% 0.90/0.92 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_r(c4, f1(c4))),
% 0.90/0.92 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 0.90/0.92 tff(1340,plain,
% 0.90/0.92 ((~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_r(c4, f1(c4))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1339, 709, 5, 1244])).
% 0.90/0.92 tff(1341,plain,
% 0.90/0.92 (big_r(f5(c2), f6(c2))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1340, 3, 1104])).
% 0.90/0.92 tff(1342,plain,
% 0.90/0.92 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(1343,plain,
% 0.90/0.92 ((big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> (big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(1344,plain,
% 0.90/0.92 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4))))),
% 0.90/0.92 inference(monotonicity,[status(thm)],[1343])).
% 0.90/0.92 tff(1345,plain,
% 0.90/0.92 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)))),
% 0.90/0.92 inference(transitivity,[status(thm)],[1344, 1342])).
% 0.90/0.92 tff(1346,plain,
% 0.90/0.92 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.90/0.92 inference(quant_inst,[status(thm)],[])).
% 0.90/0.92 tff(1347,plain,
% 0.90/0.92 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4))),
% 0.90/0.92 inference(modus_ponens,[status(thm)],[1346, 1345])).
% 0.90/0.92 tff(1348,plain,
% 0.90/0.92 ((~big_p(c1)) | big_p(f2(c2)) | big_r(c4, f3(c4))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1347, 732, 5, 1244])).
% 0.90/0.92 tff(1349,plain,
% 0.90/0.92 (big_p(f2(c2))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1348, 361, 1104])).
% 0.90/0.92 tff(1350,plain,
% 0.90/0.92 (big_r(c4, f1(c4))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[76, 361])).
% 0.90/0.92 tff(1351,plain,
% 0.90/0.92 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(1352,plain,
% 0.90/0.92 ((big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2))) <=> (big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(1353,plain,
% 0.90/0.92 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(c4, f3(c4))))),
% 0.90/0.92 inference(monotonicity,[status(thm)],[1352])).
% 0.90/0.92 tff(1354,plain,
% 0.90/0.92 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)))),
% 0.90/0.92 inference(transitivity,[status(thm)],[1353, 1351])).
% 0.90/0.92 tff(1355,plain,
% 0.90/0.92 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))),
% 0.90/0.92 inference(quant_inst,[status(thm)],[])).
% 0.90/0.92 tff(1356,plain,
% 0.90/0.92 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(c4, f3(c4))),
% 0.90/0.92 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 0.90/0.92 tff(1357,plain,
% 0.90/0.92 (big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(c4, f3(c4))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1356, 774, 5, 1244])).
% 0.90/0.92 tff(1358,plain,
% 0.90/0.92 (big_r(f1(c2), f2(c2))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1357, 361, 1104])).
% 0.90/0.92 tff(1359,plain,
% 0.90/0.92 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(1360,plain,
% 0.90/0.92 ((big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2))) <=> (big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(1361,plain,
% 0.90/0.92 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(c4, f3(c4))))),
% 0.90/0.92 inference(monotonicity,[status(thm)],[1360])).
% 0.90/0.92 tff(1362,plain,
% 0.90/0.92 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)))),
% 0.90/0.92 inference(transitivity,[status(thm)],[1361, 1359])).
% 0.90/0.92 tff(1363,plain,
% 0.90/0.92 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))),
% 0.90/0.92 inference(quant_inst,[status(thm)],[])).
% 0.90/0.92 tff(1364,plain,
% 0.90/0.92 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(c4, f3(c4))),
% 0.90/0.92 inference(modus_ponens,[status(thm)],[1363, 1362])).
% 0.90/0.92 tff(1365,plain,
% 0.90/0.92 (big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(c4, f3(c4))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1364, 753, 5, 1244])).
% 0.90/0.92 tff(1366,plain,
% 0.90/0.92 (big_r(c2, f1(c2))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1365, 361, 1104])).
% 0.90/0.92 tff(1367,plain,
% 0.90/0.92 (~big_p(f2(c4))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[226, 196, 1366, 1358, 1084, 1350, 1349])).
% 0.90/0.92 tff(1368,plain,
% 0.90/0.92 ($false),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[367, 112, 5, 361, 1367])).
% 0.90/0.92 tff(1369,plain,(big_r(c4, f3(c4)) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.92 tff(1370,plain,
% 0.90/0.92 (big_r(c4, f3(c4))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1369, 5])).
% 0.90/0.92 tff(1371,plain,
% 0.90/0.92 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(1372,plain,
% 0.90/0.92 (((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2)))) <=> ((~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(1373,plain,
% 0.90/0.92 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2)))))),
% 0.90/0.92 inference(monotonicity,[status(thm)],[1372])).
% 0.90/0.92 tff(1374,plain,
% 0.90/0.92 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.90/0.92 inference(transitivity,[status(thm)],[1373, 1371])).
% 0.90/0.92 tff(1375,plain,
% 0.90/0.92 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))),
% 0.90/0.92 inference(quant_inst,[status(thm)],[])).
% 0.90/0.92 tff(1376,plain,
% 0.90/0.92 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2)))),
% 0.90/0.92 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 0.90/0.92 tff(1377,plain,
% 0.90/0.92 (~big_p(f4(c4))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1376, 196, 1370, 98, 1341, 1333, 1325])).
% 0.90/0.92 tff(1378,plain,
% 0.90/0.92 ($false),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[348, 48, 5, 3, 1377])).
% 0.90/0.92 tff(1379,plain,(big_r(c4, f1(c4)) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.92 tff(1380,plain,
% 0.90/0.92 (big_r(c4, f1(c4))),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[1379, 5])).
% 0.90/0.92 tff(1381,plain,
% 0.90/0.92 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(1382,plain,
% 0.90/0.92 ((big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))) <=> (big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(1383,plain,
% 0.90/0.92 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4))))),
% 0.90/0.92 inference(monotonicity,[status(thm)],[1382])).
% 0.90/0.92 tff(1384,plain,
% 0.90/0.92 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.92 inference(transitivity,[status(thm)],[1383, 1381])).
% 0.90/0.92 tff(1385,plain,
% 0.90/0.92 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.92 inference(quant_inst,[status(thm)],[])).
% 0.90/0.92 tff(1386,plain,
% 0.90/0.92 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4))),
% 0.90/0.92 inference(modus_ponens,[status(thm)],[1385, 1384])).
% 0.90/0.92 tff(1387,plain,
% 0.90/0.92 ((~big_p(c1)) | big_p(f6(c2)) | big_r(f1(c4), f2(c4))),
% 0.90/0.93 inference(unit_resolution,[status(thm)],[1386, 593, 5, 1244])).
% 0.90/0.93 tff(1388,plain,
% 0.90/0.93 (big_p(f6(c2))),
% 0.90/0.93 inference(unit_resolution,[status(thm)],[1387, 258, 1104])).
% 0.90/0.93 tff(1389,plain,
% 0.90/0.93 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.93 inference(rewrite,[status(thm)],[])).
% 0.90/0.93 tff(1390,plain,
% 0.90/0.93 ((big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)) | big_r(f1(c4), f2(c4))) <=> (big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.93 inference(rewrite,[status(thm)],[])).
% 0.90/0.93 tff(1391,plain,
% 0.90/0.93 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4))))),
% 0.90/0.93 inference(monotonicity,[status(thm)],[1390])).
% 0.90/0.93 tff(1392,plain,
% 0.90/0.93 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.93 inference(transitivity,[status(thm)],[1391, 1389])).
% 0.90/0.93 tff(1393,plain,
% 0.90/0.93 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.93 inference(quant_inst,[status(thm)],[])).
% 0.90/0.93 tff(1394,plain,
% 0.90/0.93 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4))),
% 0.90/0.93 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 0.90/0.93 tff(1395,plain,
% 0.90/0.93 ((~big_p(c1)) | big_r(c2, f5(c2)) | big_r(f1(c4), f2(c4))),
% 0.90/0.93 inference(unit_resolution,[status(thm)],[1394, 614, 5, 1244])).
% 0.90/0.93 tff(1396,plain,
% 0.90/0.93 (big_r(c2, f5(c2))),
% 0.90/0.93 inference(unit_resolution,[status(thm)],[1395, 258, 1104])).
% 0.90/0.93 tff(1397,plain,
% 0.90/0.93 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.93 inference(rewrite,[status(thm)],[])).
% 0.90/0.93 tff(1398,plain,
% 0.90/0.93 ((big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_r(f1(c4), f2(c4))) <=> (big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.93 inference(rewrite,[status(thm)],[])).
% 0.90/0.93 tff(1399,plain,
% 0.90/0.93 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4))))),
% 0.90/0.93 inference(monotonicity,[status(thm)],[1398])).
% 0.90/0.93 tff(1400,plain,
% 0.90/0.93 (((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.93 inference(transitivity,[status(thm)],[1399, 1397])).
% 0.90/0.93 tff(1401,plain,
% 0.90/0.93 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_r(f1(c4), f2(c4)))),
% 0.90/0.93 inference(quant_inst,[status(thm)],[])).
% 0.90/0.93 tff(1402,plain,
% 0.90/0.93 ((~![X2: $i, X7: $i, X1: $i] : (big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4))),
% 0.90/0.93 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 0.90/0.93 tff(1403,plain,
% 0.90/0.93 ((~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_r(f1(c4), f2(c4))),
% 0.90/0.93 inference(unit_resolution,[status(thm)],[1402, 635, 5, 1244])).
% 0.90/0.93 tff(1404,plain,
% 0.90/0.93 (big_r(f5(c2), f6(c2))),
% 0.90/0.93 inference(unit_resolution,[status(thm)],[1403, 258, 1104])).
% 0.90/0.93 tff(1405,plain,
% 0.90/0.93 (~big_p(f4(c4))),
% 0.90/0.93 inference(unit_resolution,[status(thm)],[1376, 196, 1370, 314, 1404, 1396, 1388])).
% 0.90/0.93 tff(1406,plain,
% 0.90/0.93 ($false),
% 0.90/0.93 inference(unit_resolution,[status(thm)],[277, 271, 5, 258, 1405])).
% 0.90/0.93 tff(1407,plain,(big_r(f1(c4), f2(c4)) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.93 tff(1408,plain,
% 0.90/0.93 (big_r(f1(c4), f2(c4))),
% 0.90/0.93 inference(unit_resolution,[status(thm)],[1407, 5])).
% 0.90/0.93 tff(1409,plain,
% 0.90/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_p(f4(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_p(f4(c4)))),
% 0.90/0.93 inference(rewrite,[status(thm)],[])).
% 0.90/0.93 tff(1410,plain,
% 0.90/0.93 ((big_p(f4(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2))) <=> (big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_p(f4(c4)))),
% 0.90/0.93 inference(rewrite,[status(thm)],[])).
% 0.90/0.93 tff(1411,plain,
% 0.90/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_p(f4(c4))))),
% 0.90/0.93 inference(monotonicity,[status(thm)],[1410])).
% 0.90/0.93 tff(1412,plain,
% 0.90/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_p(f4(c4)))),
% 0.90/0.93 inference(transitivity,[status(thm)],[1411, 1409])).
% 0.90/0.93 tff(1413,plain,
% 0.90/0.93 ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(f4(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))),
% 0.90/0.93 inference(quant_inst,[status(thm)],[])).
% 0.90/0.93 tff(1414,plain,
% 0.90/0.93 ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_p(f4(c4))),
% 0.90/0.93 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 0.90/0.93 tff(1415,plain,
% 0.90/0.93 (big_r(f1(c2), f2(c2)) | big_p(f4(c4))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1414, 572, 1104, 5, 1244])).
% 0.97/0.93 tff(1416,plain,
% 0.97/0.93 (big_r(f1(c2), f2(c2))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1415, 1144])).
% 0.97/0.93 tff(1417,plain,
% 0.97/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_p(f4(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_p(f4(c4)))),
% 0.97/0.93 inference(rewrite,[status(thm)],[])).
% 0.97/0.93 tff(1418,plain,
% 0.97/0.93 ((big_p(f4(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2))) <=> (big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_p(f4(c4)))),
% 0.97/0.93 inference(rewrite,[status(thm)],[])).
% 0.97/0.93 tff(1419,plain,
% 0.97/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(f4(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_p(f4(c4))))),
% 0.97/0.93 inference(monotonicity,[status(thm)],[1418])).
% 0.97/0.93 tff(1420,plain,
% 0.97/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(f4(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_p(f4(c4)))),
% 0.97/0.93 inference(transitivity,[status(thm)],[1419, 1417])).
% 0.97/0.93 tff(1421,plain,
% 0.97/0.93 ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(f4(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))),
% 0.97/0.93 inference(quant_inst,[status(thm)],[])).
% 0.97/0.93 tff(1422,plain,
% 0.97/0.93 ((~![X7: $i, X8: $i, X1: $i] : (big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_p(f4(c4))),
% 0.97/0.93 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 0.97/0.93 tff(1423,plain,
% 0.97/0.93 (big_r(c2, f1(c2)) | big_p(f4(c4))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1422, 551, 1104, 5, 1244])).
% 0.97/0.93 tff(1424,plain,
% 0.97/0.93 (big_r(c2, f1(c2))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1423, 1144])).
% 0.97/0.93 tff(1425,plain,
% 0.97/0.93 ($false),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[226, 196, 1424, 1416, 1408, 1380, 1317, 1315])).
% 0.97/0.93 tff(1426,plain,(big_p(f4(c4)) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.97/0.93 tff(1427,plain,
% 0.97/0.93 (big_p(f4(c4))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1426, 5])).
% 0.97/0.93 tff(1428,plain,
% 0.97/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)))),
% 0.97/0.93 inference(rewrite,[status(thm)],[])).
% 0.97/0.93 tff(1429,plain,
% 0.97/0.93 ((big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> (big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)))),
% 0.97/0.93 inference(rewrite,[status(thm)],[])).
% 0.97/0.93 tff(1430,plain,
% 0.97/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4))))),
% 0.97/0.93 inference(monotonicity,[status(thm)],[1429])).
% 0.97/0.93 tff(1431,plain,
% 0.97/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)))),
% 0.97/0.93 inference(transitivity,[status(thm)],[1430, 1428])).
% 0.97/0.93 tff(1432,plain,
% 0.97/0.93 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.97/0.93 inference(quant_inst,[status(thm)],[])).
% 0.97/0.93 tff(1433,plain,
% 0.97/0.93 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | big_p(c4) | (~big_p(c1)) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4))),
% 0.97/0.93 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 0.97/0.93 tff(1434,plain,
% 0.97/0.93 ((~big_p(c1)) | big_p(f2(c2)) | big_r(f3(c4), f4(c4))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1433, 805, 5, 1244])).
% 0.97/0.93 tff(1435,plain,
% 0.97/0.93 (big_p(f2(c2))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1434, 1110, 1104])).
% 0.97/0.93 tff(1436,plain,
% 0.97/0.93 (big_p(f2(c4))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[419, 1110])).
% 0.97/0.93 tff(1437,plain,
% 0.97/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)))),
% 0.97/0.93 inference(rewrite,[status(thm)],[])).
% 0.97/0.93 tff(1438,plain,
% 0.97/0.93 ((big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2))) <=> (big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)))),
% 0.97/0.93 inference(rewrite,[status(thm)],[])).
% 0.97/0.93 tff(1439,plain,
% 0.97/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4))))),
% 0.97/0.93 inference(monotonicity,[status(thm)],[1438])).
% 0.97/0.93 tff(1440,plain,
% 0.97/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)))),
% 0.97/0.93 inference(transitivity,[status(thm)],[1439, 1437])).
% 0.97/0.93 tff(1441,plain,
% 0.97/0.93 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))),
% 0.97/0.93 inference(quant_inst,[status(thm)],[])).
% 0.97/0.93 tff(1442,plain,
% 0.97/0.93 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4))),
% 0.97/0.93 inference(modus_ponens,[status(thm)],[1441, 1440])).
% 0.97/0.93 tff(1443,plain,
% 0.97/0.93 (big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(f3(c4), f4(c4))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1442, 847, 5, 1244])).
% 0.97/0.93 tff(1444,plain,
% 0.97/0.93 (big_r(f1(c2), f2(c2))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1443, 1110, 1104])).
% 0.97/0.93 tff(1445,plain,
% 0.97/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)))),
% 0.97/0.93 inference(rewrite,[status(thm)],[])).
% 0.97/0.93 tff(1446,plain,
% 0.97/0.93 ((big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2))) <=> (big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)))),
% 0.97/0.93 inference(rewrite,[status(thm)],[])).
% 0.97/0.93 tff(1447,plain,
% 0.97/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4))))),
% 0.97/0.93 inference(monotonicity,[status(thm)],[1446])).
% 0.97/0.93 tff(1448,plain,
% 0.97/0.93 (((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)))),
% 0.97/0.93 inference(transitivity,[status(thm)],[1447, 1445])).
% 0.97/0.93 tff(1449,plain,
% 0.97/0.93 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))),
% 0.97/0.93 inference(quant_inst,[status(thm)],[])).
% 0.97/0.93 tff(1450,plain,
% 0.97/0.93 ((~![X7: $i, X8: $i, X1: $i] : (big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | big_p(c4) | big_r(c2, f1(c2)) | (~big_p(c1)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4))),
% 0.97/0.93 inference(modus_ponens,[status(thm)],[1449, 1448])).
% 0.97/0.93 tff(1451,plain,
% 0.97/0.93 (big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(f3(c4), f4(c4))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1450, 826, 5, 1244])).
% 0.97/0.93 tff(1452,plain,
% 0.97/0.93 (big_r(c2, f1(c2))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1451, 1110, 1104])).
% 0.97/0.93 tff(1453,plain,
% 0.97/0.93 ($false),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[226, 196, 1452, 1444, 1408, 1380, 1436, 1435])).
% 0.97/0.93 tff(1454,plain,(big_r(f3(c4), f4(c4)) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.97/0.93 tff(1455,plain,
% 0.97/0.93 (big_r(f3(c4), f4(c4))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1454, 5])).
% 0.97/0.93 tff(1456,plain,
% 0.97/0.93 ($false),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1376, 196, 1370, 1455, 1427, 1307, 1286, 1265])).
% 0.97/0.93 tff(1457,plain,(big_p(f2(c4)) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.97/0.93 tff(1458,plain,
% 0.97/0.93 (big_p(f2(c4))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1457, 5])).
% 0.97/0.93 tff(1459,assumption,(big_p(c1)), introduced(assumption)).
% 0.97/0.93 tff(1460,assumption,(~big_p(f6(c2))), introduced(assumption)).
% 0.97/0.93 tff(1461,plain,
% 0.97/0.93 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c1)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c1)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)))),
% 0.97/0.93 inference(rewrite,[status(thm)],[])).
% 0.97/0.93 tff(1462,plain,
% 0.97/0.93 ((big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(c1)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)))),
% 0.97/0.93 inference(rewrite,[status(thm)],[])).
% 0.97/0.93 tff(1463,plain,
% 0.97/0.93 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c1)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1))))),
% 0.97/0.93 inference(monotonicity,[status(thm)],[1462])).
% 0.97/0.93 tff(1464,plain,
% 0.97/0.93 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c1)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)))),
% 0.97/0.93 inference(transitivity,[status(thm)],[1463, 1461])).
% 0.97/0.93 tff(1465,plain,
% 0.97/0.93 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.97/0.93 inference(quant_inst,[status(thm)],[])).
% 0.97/0.93 tff(1466,plain,
% 0.97/0.93 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c1)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1))),
% 0.97/0.93 inference(modus_ponens,[status(thm)],[1465, 1464])).
% 0.97/0.93 tff(1467,plain,
% 0.97/0.93 ((~big_p(c1)) | big_p(f6(c2)) | big_p(f2(c2))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1466, 873, 1244])).
% 0.97/0.93 tff(1468,plain,
% 0.97/0.93 (big_p(f2(c2))),
% 0.97/0.93 inference(unit_resolution,[status(thm)],[1467, 1460, 1459])).
% 0.97/0.93 tff(1469,assumption,(big_p(f2(c4))), introduced(assumption)).
% 0.97/0.93 tff(1470,assumption,(big_r(c4, f1(c4))), introduced(assumption)).
% 0.97/0.93 tff(1471,assumption,(big_r(f1(c4), f2(c4))), introduced(assumption)).
% 0.97/0.93 tff(1472,plain,
% 0.97/0.93 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)))),
% 0.97/0.93 inference(rewrite,[status(thm)],[])).
% 0.97/0.93 tff(1473,plain,
% 0.97/0.93 ((big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2))) <=> (big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)))),
% 0.97/0.93 inference(rewrite,[status(thm)],[])).
% 0.97/0.93 tff(1474,plain,
% 0.97/0.93 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1))))),
% 0.97/0.93 inference(monotonicity,[status(thm)],[1473])).
% 0.97/0.93 tff(1475,plain,
% 0.97/0.93 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)))),
% 0.97/0.93 inference(transitivity,[status(thm)],[1474, 1472])).
% 0.97/0.93 tff(1476,plain,
% 0.97/0.93 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))),
% 0.97/0.94 inference(quant_inst,[status(thm)],[])).
% 0.97/0.94 tff(1477,plain,
% 0.97/0.94 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1))),
% 0.97/0.94 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 0.97/0.94 tff(1478,plain,
% 0.97/0.94 (big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_p(f6(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1477, 942, 1244])).
% 0.97/0.94 tff(1479,plain,
% 0.97/0.94 (big_r(f1(c2), f2(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1478, 1460, 1459])).
% 0.97/0.94 tff(1480,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f1(c2)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(rewrite,[status(thm)],[])).
% 0.97/0.94 tff(1481,plain,
% 0.97/0.94 ((big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> (big_r(c2, f1(c2)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(rewrite,[status(thm)],[])).
% 0.97/0.94 tff(1482,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f1(c2)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1))))),
% 0.97/0.94 inference(monotonicity,[status(thm)],[1481])).
% 0.97/0.94 tff(1483,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(transitivity,[status(thm)],[1482, 1480])).
% 0.97/0.94 tff(1484,plain,
% 0.97/0.94 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.97/0.94 inference(quant_inst,[status(thm)],[])).
% 0.97/0.94 tff(1485,plain,
% 0.97/0.94 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c2, c1))),
% 0.97/0.94 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 0.97/0.94 tff(1486,plain,
% 0.97/0.94 (big_r(c2, f1(c2)) | (~big_p(c1)) | big_p(f6(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1485, 1009, 1244])).
% 0.97/0.94 tff(1487,plain,
% 0.97/0.94 (big_p(f6(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1486, 1, 1459])).
% 0.97/0.94 tff(1488,assumption,(~big_r(c2, f5(c2))), introduced(assumption)).
% 0.97/0.94 tff(1489,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c1)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c1)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(rewrite,[status(thm)],[])).
% 0.97/0.94 tff(1490,plain,
% 0.97/0.94 ((big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(c1)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(rewrite,[status(thm)],[])).
% 0.97/0.94 tff(1491,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c1)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1))))),
% 0.97/0.94 inference(monotonicity,[status(thm)],[1490])).
% 0.97/0.94 tff(1492,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c1)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(transitivity,[status(thm)],[1491, 1489])).
% 0.97/0.94 tff(1493,plain,
% 0.97/0.94 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.97/0.94 inference(quant_inst,[status(thm)],[])).
% 0.97/0.94 tff(1494,plain,
% 0.97/0.94 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c1)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1))),
% 0.97/0.94 inference(modus_ponens,[status(thm)],[1493, 1492])).
% 0.97/0.94 tff(1495,plain,
% 0.97/0.94 ((~big_p(c1)) | big_r(c2, f5(c2)) | big_p(f2(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1494, 894, 1244])).
% 0.97/0.94 tff(1496,plain,
% 0.97/0.94 (big_p(f2(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1495, 1488, 1459])).
% 0.97/0.94 tff(1497,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(rewrite,[status(thm)],[])).
% 0.97/0.94 tff(1498,plain,
% 0.97/0.94 ((big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2))) <=> (big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(rewrite,[status(thm)],[])).
% 0.97/0.94 tff(1499,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1))))),
% 0.97/0.94 inference(monotonicity,[status(thm)],[1498])).
% 0.97/0.94 tff(1500,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(transitivity,[status(thm)],[1499, 1497])).
% 0.97/0.94 tff(1501,plain,
% 0.97/0.94 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))),
% 0.97/0.94 inference(quant_inst,[status(thm)],[])).
% 0.97/0.94 tff(1502,plain,
% 0.97/0.94 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1))),
% 0.97/0.94 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 0.97/0.94 tff(1503,plain,
% 0.97/0.94 (big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(c2, f5(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1502, 963, 1244])).
% 0.97/0.94 tff(1504,plain,
% 0.97/0.94 (big_r(f1(c2), f2(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1503, 1488, 1459])).
% 0.97/0.94 tff(1505,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(rewrite,[status(thm)],[])).
% 0.97/0.94 tff(1506,plain,
% 0.97/0.94 ((big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> (big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(rewrite,[status(thm)],[])).
% 0.97/0.94 tff(1507,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1))))),
% 0.97/0.94 inference(monotonicity,[status(thm)],[1506])).
% 0.97/0.94 tff(1508,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(transitivity,[status(thm)],[1507, 1505])).
% 0.97/0.94 tff(1509,plain,
% 0.97/0.94 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.97/0.94 inference(quant_inst,[status(thm)],[])).
% 0.97/0.94 tff(1510,plain,
% 0.97/0.94 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c2, c1))),
% 0.97/0.94 inference(modus_ponens,[status(thm)],[1509, 1508])).
% 0.97/0.94 tff(1511,plain,
% 0.97/0.94 (big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(c2, f5(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1510, 1030, 1244])).
% 0.97/0.94 tff(1512,plain,
% 0.97/0.94 (big_r(c2, f1(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1511, 1488, 1459])).
% 0.97/0.94 tff(1513,plain,
% 0.97/0.94 ($false),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[226, 196, 1512, 1504, 1471, 1470, 1469, 1496])).
% 0.97/0.94 tff(1514,plain,(big_r(c2, f5(c2)) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_p(f2(c4))) | (~big_p(c1))), inference(lemma,lemma(discharge,[]))).
% 0.97/0.94 tff(1515,plain,
% 0.97/0.94 (big_r(c2, f5(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1514, 1471, 1470, 1469, 1459])).
% 0.97/0.94 tff(1516,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(rewrite,[status(thm)],[])).
% 0.97/0.94 tff(1517,plain,
% 0.97/0.94 ((big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> (big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(rewrite,[status(thm)],[])).
% 0.97/0.94 tff(1518,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1))))),
% 0.97/0.94 inference(monotonicity,[status(thm)],[1517])).
% 0.97/0.94 tff(1519,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(transitivity,[status(thm)],[1518, 1516])).
% 0.97/0.94 tff(1520,plain,
% 0.97/0.94 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.97/0.94 inference(quant_inst,[status(thm)],[])).
% 0.97/0.94 tff(1521,plain,
% 0.97/0.94 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1))),
% 0.97/0.94 inference(modus_ponens,[status(thm)],[1520, 1519])).
% 0.97/0.94 tff(1522,plain,
% 0.97/0.94 (big_r(c2, f1(c2)) | (~big_p(c1)) | big_r(f5(c2), f6(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1521, 1051, 1244])).
% 0.97/0.94 tff(1523,plain,
% 0.97/0.94 (big_r(f5(c2), f6(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1522, 1, 1459])).
% 0.97/0.94 tff(1524,plain,
% 0.97/0.94 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.97/0.94 inference(rewrite,[status(thm)],[])).
% 0.97/0.94 tff(1525,plain,
% 0.97/0.94 (((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2)))) <=> ((~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.97/0.94 inference(rewrite,[status(thm)],[])).
% 0.97/0.94 tff(1526,plain,
% 0.97/0.94 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2)))))),
% 0.97/0.94 inference(monotonicity,[status(thm)],[1525])).
% 0.97/0.94 tff(1527,plain,
% 0.97/0.94 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.97/0.94 inference(transitivity,[status(thm)],[1526, 1524])).
% 0.97/0.94 tff(1528,plain,
% 0.97/0.94 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))),
% 0.97/0.94 inference(quant_inst,[status(thm)],[])).
% 0.97/0.94 tff(1529,plain,
% 0.97/0.94 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2)))),
% 0.97/0.94 inference(modus_ponens,[status(thm)],[1528, 1527])).
% 0.97/0.94 tff(1530,plain,
% 0.97/0.94 ($false),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1529, 196, 1471, 1470, 1469, 1523, 1515, 1487])).
% 0.97/0.94 tff(1531,plain,(big_r(c2, f1(c2)) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_p(f2(c4))) | (~big_p(c1))), inference(lemma,lemma(discharge,[]))).
% 0.97/0.94 tff(1532,plain,
% 0.97/0.94 (big_r(c2, f1(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1531, 1471, 1470, 1469, 1459])).
% 0.97/0.94 tff(1533,plain,
% 0.97/0.94 ($false),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[226, 196, 1532, 1479, 1471, 1470, 1469, 1468])).
% 0.97/0.94 tff(1534,plain,(big_p(f6(c2)) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_p(f2(c4))) | (~big_p(c1))), inference(lemma,lemma(discharge,[]))).
% 0.97/0.94 tff(1535,plain,
% 0.97/0.94 (big_p(f6(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1534, 1408, 1380, 1458, 1104])).
% 0.97/0.94 tff(1536,plain,
% 0.97/0.94 (big_r(c2, f5(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1514, 1408, 1380, 1458, 1104])).
% 0.97/0.94 tff(1537,assumption,(big_p(f6(c2))), introduced(assumption)).
% 0.97/0.94 tff(1538,assumption,(big_r(c2, f5(c2))), introduced(assumption)).
% 0.97/0.94 tff(1539,assumption,(big_r(f5(c2), f6(c2))), introduced(assumption)).
% 0.97/0.94 tff(1540,plain,
% 0.97/0.94 ($false),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1529, 196, 1471, 1470, 1469, 1539, 1538, 1537])).
% 0.97/0.94 tff(1541,plain,((~big_r(f5(c2), f6(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_p(f2(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2)))), inference(lemma,lemma(discharge,[]))).
% 0.97/0.94 tff(1542,plain,
% 0.97/0.94 (~big_r(f5(c2), f6(c2))),
% 0.97/0.94 inference(unit_resolution,[status(thm)],[1541, 1408, 1380, 1458, 1536, 1535])).
% 0.97/0.94 tff(1543,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(rewrite,[status(thm)],[])).
% 0.97/0.94 tff(1544,plain,
% 0.97/0.94 ((big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(rewrite,[status(thm)],[])).
% 0.97/0.94 tff(1545,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1))))),
% 0.97/0.94 inference(monotonicity,[status(thm)],[1544])).
% 0.97/0.94 tff(1546,plain,
% 0.97/0.94 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)))),
% 0.97/0.94 inference(transitivity,[status(thm)],[1545, 1543])).
% 0.97/0.94 tff(1547,plain,
% 0.97/0.94 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.97/0.95 inference(quant_inst,[status(thm)],[])).
% 0.97/0.95 tff(1548,plain,
% 0.97/0.95 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 0.97/0.95 tff(1549,plain,
% 0.97/0.95 ((~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1548, 915, 1244])).
% 0.97/0.95 tff(1550,plain,
% 0.97/0.95 (big_p(f2(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1549, 1542, 1104])).
% 0.97/0.95 tff(1551,plain,
% 0.97/0.95 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1552,plain,
% 0.97/0.95 ((big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2))) <=> (big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1553,plain,
% 0.97/0.95 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1))))),
% 0.97/0.95 inference(monotonicity,[status(thm)],[1552])).
% 0.97/0.95 tff(1554,plain,
% 0.97/0.95 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)))),
% 0.97/0.95 inference(transitivity,[status(thm)],[1553, 1551])).
% 0.97/0.95 tff(1555,plain,
% 0.97/0.95 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))),
% 0.97/0.95 inference(quant_inst,[status(thm)],[])).
% 0.97/0.95 tff(1556,plain,
% 0.97/0.95 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1555, 1554])).
% 0.97/0.95 tff(1557,plain,
% 0.97/0.95 (big_r(f1(c2), f2(c2)) | (~big_p(c1)) | big_r(f5(c2), f6(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1556, 984, 1244])).
% 0.97/0.95 tff(1558,plain,
% 0.97/0.95 (big_r(f1(c2), f2(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1557, 1542, 1104])).
% 0.97/0.95 tff(1559,plain,
% 0.97/0.95 (big_r(c2, f1(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1531, 1408, 1380, 1458, 1104])).
% 0.97/0.95 tff(1560,plain,
% 0.97/0.95 ($false),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[226, 196, 1559, 1558, 1408, 1380, 1458, 1550])).
% 0.97/0.95 tff(1561,plain,(big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.97/0.95 tff(1562,plain,
% 0.97/0.95 ((big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)) <=> (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1563,plain,
% 0.97/0.95 (((big_p(c1) | (~big_p(c4)) | (~big_p(c2))) | big_r(c4, c3)) <=> (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1564,plain,
% 0.97/0.95 (((big_p(c1) | (~big_p(c2))) | (~big_p(c4))) <=> (big_p(c1) | (~big_p(c4)) | (~big_p(c2)))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1565,plain,
% 0.97/0.95 (((~big_p(c2)) | big_p(c1)) <=> (big_p(c1) | (~big_p(c2)))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1566,plain,
% 0.97/0.95 ((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) <=> ((big_p(c1) | (~big_p(c2))) | (~big_p(c4)))),
% 0.97/0.95 inference(monotonicity,[status(thm)],[1565])).
% 0.97/0.95 tff(1567,plain,
% 0.97/0.95 ((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) <=> (big_p(c1) | (~big_p(c4)) | (~big_p(c2)))),
% 0.97/0.95 inference(transitivity,[status(thm)],[1566, 1564])).
% 0.97/0.95 tff(1568,plain,
% 0.97/0.95 (((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) | big_r(c4, c3)) <=> ((big_p(c1) | (~big_p(c4)) | (~big_p(c2))) | big_r(c4, c3))),
% 0.97/0.95 inference(monotonicity,[status(thm)],[1567])).
% 0.97/0.95 tff(1569,plain,
% 0.97/0.95 (((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) | big_r(c4, c3)) <=> (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3))),
% 0.97/0.95 inference(transitivity,[status(thm)],[1568, 1563])).
% 0.97/0.95 tff(1570,axiom,((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) | big_r(c4, c3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_55')).
% 0.97/0.95 tff(1571,plain,
% 0.97/0.95 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1570, 1569])).
% 0.97/0.95 tff(1572,plain,
% 0.97/0.95 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1571, 1562])).
% 0.97/0.95 tff(1573,plain,
% 0.97/0.95 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1572, 1562])).
% 0.97/0.95 tff(1574,plain,
% 0.97/0.95 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1573, 1562])).
% 0.97/0.95 tff(1575,plain,
% 0.97/0.95 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1574, 1562])).
% 0.97/0.95 tff(1576,plain,
% 0.97/0.95 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1575, 1562])).
% 0.97/0.95 tff(1577,plain,
% 0.97/0.95 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1576, 1562])).
% 0.97/0.95 tff(1578,plain,
% 0.97/0.95 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1577, 1562])).
% 0.97/0.95 tff(1579,plain,
% 0.97/0.95 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1578, 1562])).
% 0.97/0.95 tff(1580,plain,
% 0.97/0.95 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1579, 1562])).
% 0.97/0.95 tff(1581,plain,
% 0.97/0.95 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1580, 1562])).
% 0.97/0.95 tff(1582,plain,
% 0.97/0.95 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1581, 1562])).
% 0.97/0.95 tff(1583,plain,
% 0.97/0.95 (big_r(c4, c3)),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1582, 2, 1561, 1063])).
% 0.97/0.95 tff(1584,plain,
% 0.97/0.95 ((big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))) <=> (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2)))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1585,plain,
% 0.97/0.95 (((big_p(c1) | (~big_p(c4)) | (~big_p(c2))) | big_p(c3)) <=> (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2)))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1586,plain,
% 0.97/0.95 (((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) | big_p(c3)) <=> ((big_p(c1) | (~big_p(c4)) | (~big_p(c2))) | big_p(c3))),
% 0.97/0.95 inference(monotonicity,[status(thm)],[1567])).
% 0.97/0.95 tff(1587,plain,
% 0.97/0.95 (((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) | big_p(c3)) <=> (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2)))),
% 0.97/0.95 inference(transitivity,[status(thm)],[1586, 1585])).
% 0.97/0.95 tff(1588,axiom,((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) | big_p(c3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_54')).
% 0.97/0.95 tff(1589,plain,
% 0.97/0.95 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1588, 1587])).
% 0.97/0.95 tff(1590,plain,
% 0.97/0.95 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1589, 1584])).
% 0.97/0.95 tff(1591,plain,
% 0.97/0.95 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1590, 1584])).
% 0.97/0.95 tff(1592,plain,
% 0.97/0.95 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1591, 1584])).
% 0.97/0.95 tff(1593,plain,
% 0.97/0.95 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1592, 1584])).
% 0.97/0.95 tff(1594,plain,
% 0.97/0.95 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1593, 1584])).
% 0.97/0.95 tff(1595,plain,
% 0.97/0.95 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1594, 1584])).
% 0.97/0.95 tff(1596,plain,
% 0.97/0.95 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1595, 1584])).
% 0.97/0.95 tff(1597,plain,
% 0.97/0.95 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1596, 1584])).
% 0.97/0.95 tff(1598,plain,
% 0.97/0.95 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1597, 1584])).
% 0.97/0.95 tff(1599,plain,
% 0.97/0.95 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1598, 1584])).
% 0.97/0.95 tff(1600,plain,
% 0.97/0.95 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1599, 1584])).
% 0.97/0.95 tff(1601,plain,
% 0.97/0.95 (big_p(c3)),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1600, 2, 1561, 1063])).
% 0.97/0.95 tff(1602,plain,
% 0.97/0.95 (big_r(c4, f1(c4)) | big_r(c4, f5(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1036, 1030, 1601, 1583])).
% 0.97/0.95 tff(1603,plain,
% 0.97/0.95 (big_r(c4, f5(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1602, 3])).
% 0.97/0.95 tff(1604,plain,
% 0.97/0.95 (big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1057, 1051, 1601, 1583])).
% 0.97/0.95 tff(1605,plain,
% 0.97/0.95 (big_r(f5(c4), f6(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1604, 3])).
% 0.97/0.95 tff(1606,plain,
% 0.97/0.95 (big_r(c4, f1(c4)) | big_p(f6(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1015, 1009, 1601, 1583])).
% 0.97/0.95 tff(1607,plain,
% 0.97/0.95 (big_p(f6(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1606, 3])).
% 0.97/0.95 tff(1608,plain,
% 0.97/0.95 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_p(c2)) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1609,plain,
% 0.97/0.95 ((big_p(c1) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4)))) <=> (big_p(c1) | (~big_p(c2)) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1610,plain,
% 0.97/0.95 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_p(c2)) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4)))))),
% 0.97/0.95 inference(monotonicity,[status(thm)],[1609])).
% 0.97/0.95 tff(1611,plain,
% 0.97/0.95 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.97/0.95 inference(transitivity,[status(thm)],[1610, 1608])).
% 0.97/0.95 tff(1612,plain,
% 0.97/0.95 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4))))),
% 0.97/0.95 inference(quant_inst,[status(thm)],[])).
% 0.97/0.95 tff(1613,plain,
% 0.97/0.95 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4)))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1612, 1611])).
% 0.97/0.95 tff(1614,plain,
% 0.97/0.95 ($false),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1613, 2, 1063, 1073, 1607, 1605, 1603])).
% 0.97/0.95 tff(1615,plain,(big_r(c4, f1(c4)) | big_p(c1)), inference(lemma,lemma(discharge,[]))).
% 0.97/0.95 tff(1616,plain,
% 0.97/0.95 (big_r(c4, f1(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1615, 2])).
% 0.97/0.95 tff(1617,plain,
% 0.97/0.95 (big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[969, 963, 1601, 1583])).
% 0.97/0.95 tff(1618,plain,
% 0.97/0.95 (big_r(c4, f5(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1617, 258])).
% 0.97/0.95 tff(1619,plain,
% 0.97/0.95 (big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[990, 984, 1601, 1583])).
% 0.97/0.95 tff(1620,plain,
% 0.97/0.95 (big_r(f5(c4), f6(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1619, 258])).
% 0.97/0.95 tff(1621,plain,
% 0.97/0.95 (big_r(f1(c4), f2(c4)) | big_p(f6(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[948, 942, 1601, 1583])).
% 0.97/0.95 tff(1622,plain,
% 0.97/0.95 (big_p(f6(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1621, 258])).
% 0.97/0.95 tff(1623,plain,
% 0.97/0.95 ($false),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1613, 2, 1063, 1073, 1622, 1620, 1618])).
% 0.97/0.95 tff(1624,plain,(big_r(f1(c4), f2(c4)) | big_p(c1)), inference(lemma,lemma(discharge,[]))).
% 0.97/0.95 tff(1625,plain,
% 0.97/0.95 (big_r(f1(c4), f2(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1624, 2])).
% 0.97/0.95 tff(1626,plain,
% 0.97/0.95 ((~big_p(f2(c4))) | (~big_r(c4, f1(c4)))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1090, 2, 1063, 1073, 1625])).
% 0.97/0.95 tff(1627,plain,
% 0.97/0.95 (~big_p(f2(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1626, 1616])).
% 0.97/0.95 tff(1628,plain,
% 0.97/0.95 (big_r(c4, f5(c4)) | big_p(f2(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[900, 894, 1601, 1583])).
% 0.97/0.95 tff(1629,plain,
% 0.97/0.95 (big_r(c4, f5(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1628, 1627])).
% 0.97/0.95 tff(1630,plain,
% 0.97/0.95 (big_r(f5(c4), f6(c4)) | big_p(f2(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[921, 915, 1601, 1583])).
% 0.97/0.95 tff(1631,plain,
% 0.97/0.95 (big_r(f5(c4), f6(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1630, 1627])).
% 0.97/0.95 tff(1632,plain,
% 0.97/0.95 (big_p(f6(c4)) | big_p(f2(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[879, 873, 1601, 1583])).
% 0.97/0.95 tff(1633,plain,
% 0.97/0.95 (big_p(f6(c4))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1632, 1627])).
% 0.97/0.95 tff(1634,plain,
% 0.97/0.95 ($false),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1613, 2, 1063, 1073, 1633, 1631, 1629])).
% 0.97/0.95 tff(1635,plain,(big_p(c1)), inference(lemma,lemma(discharge,[]))).
% 0.97/0.95 tff(1636,plain,
% 0.97/0.95 (big_r(c2, f1(c2)) | big_p(f6(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1486, 1635])).
% 0.97/0.95 tff(1637,plain,
% 0.97/0.95 (big_p(f6(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1636, 1])).
% 0.97/0.95 tff(1638,plain,
% 0.97/0.95 (big_r(c2, f1(c2)) | big_r(c2, f5(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1511, 1635])).
% 0.97/0.95 tff(1639,plain,
% 0.97/0.95 (big_r(c2, f5(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1638, 1])).
% 0.97/0.95 tff(1640,plain,
% 0.97/0.95 (big_r(c2, f1(c2)) | big_r(f5(c2), f6(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1522, 1635])).
% 0.97/0.95 tff(1641,plain,
% 0.97/0.95 (big_r(f5(c2), f6(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1640, 1])).
% 0.97/0.95 tff(1642,plain,
% 0.97/0.95 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(c4)) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1643,plain,
% 0.97/0.95 ((big_p(c3) | (~big_p(f6(c2))) | (~big_p(c4)) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2)))) <=> (big_p(c3) | (~big_p(c4)) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1644,plain,
% 0.97/0.95 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f6(c2))) | (~big_p(c4)) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(c4)) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2)))))),
% 0.97/0.95 inference(monotonicity,[status(thm)],[1643])).
% 0.97/0.95 tff(1645,plain,
% 0.97/0.95 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f6(c2))) | (~big_p(c4)) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.97/0.95 inference(transitivity,[status(thm)],[1644, 1642])).
% 0.97/0.95 tff(1646,plain,
% 0.97/0.95 ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f6(c2))) | (~big_p(c4)) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.97/0.95 inference(quant_inst,[status(thm)],[])).
% 0.97/0.95 tff(1647,plain,
% 0.97/0.95 ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2)))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 0.97/0.95 tff(1648,plain,
% 0.97/0.95 ($false),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1647, 472, 1561, 485, 1539, 1538, 1537])).
% 0.97/0.95 tff(1649,plain,((~big_r(f5(c2), f6(c2))) | big_p(c3) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2)))), inference(lemma,lemma(discharge,[]))).
% 0.97/0.95 tff(1650,plain,
% 0.97/0.95 (big_p(c3)),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1649, 1641, 1639, 1637])).
% 0.97/0.95 tff(1651,plain,
% 0.97/0.95 (big_p(f6(c2)) | big_p(f2(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1467, 1635])).
% 0.97/0.95 tff(1652,plain,
% 0.97/0.95 (big_p(f2(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1651, 1460])).
% 0.97/0.95 tff(1653,plain,
% 0.97/0.95 (big_r(f1(c2), f2(c2)) | big_p(f6(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1478, 1635])).
% 0.97/0.95 tff(1654,plain,
% 0.97/0.95 (big_r(f1(c2), f2(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1653, 1460])).
% 0.97/0.95 tff(1655,plain,
% 0.97/0.95 (big_r(c2, f1(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1636, 1460])).
% 0.97/0.95 tff(1656,plain,
% 0.97/0.95 ($false),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[448, 1561, 431, 442, 1655, 1654, 1652])).
% 0.97/0.95 tff(1657,plain,(big_p(f6(c2)) | big_r(c4, c3)), inference(lemma,lemma(discharge,[]))).
% 0.97/0.95 tff(1658,plain,
% 0.97/0.95 (big_p(f6(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1657, 431])).
% 0.97/0.95 tff(1659,plain,
% 0.97/0.95 (big_r(c2, f5(c2)) | big_p(f2(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1495, 1635])).
% 0.97/0.95 tff(1660,plain,
% 0.97/0.95 (big_p(f2(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1659, 1488])).
% 0.97/0.95 tff(1661,plain,
% 0.97/0.95 (big_r(f1(c2), f2(c2)) | big_r(c2, f5(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1503, 1635])).
% 0.97/0.95 tff(1662,plain,
% 0.97/0.95 (big_r(f1(c2), f2(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1661, 1488])).
% 0.97/0.95 tff(1663,plain,
% 0.97/0.95 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(c4)) | big_r(c4, c3) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1664,plain,
% 0.97/0.95 (((~big_p(f6(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2)))) <=> ((~big_p(c4)) | big_r(c4, c3) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1665,plain,
% 0.97/0.95 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f6(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(c4)) | big_r(c4, c3) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2)))))),
% 0.97/0.95 inference(monotonicity,[status(thm)],[1664])).
% 0.97/0.95 tff(1666,plain,
% 0.97/0.95 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f6(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.97/0.95 inference(transitivity,[status(thm)],[1665, 1663])).
% 0.97/0.95 tff(1667,plain,
% 0.97/0.95 ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f6(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.97/0.95 inference(quant_inst,[status(thm)],[])).
% 0.97/0.95 tff(1668,plain,
% 0.97/0.95 ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2)))),
% 0.97/0.95 inference(modus_ponens,[status(thm)],[1667, 1666])).
% 0.97/0.95 tff(1669,plain,
% 0.97/0.95 ($false),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1668, 1561, 431, 442, 1641, 1639, 1658])).
% 0.97/0.95 tff(1670,plain,(big_r(c2, f1(c2)) | big_r(c4, c3)), inference(lemma,lemma(discharge,[]))).
% 0.97/0.95 tff(1671,plain,
% 0.97/0.95 (big_r(c2, f1(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1670, 431])).
% 0.97/0.95 tff(1672,plain,
% 0.97/0.95 ($false),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[448, 1561, 431, 442, 1671, 1662, 1660])).
% 0.97/0.95 tff(1673,plain,(big_r(c2, f5(c2)) | big_r(c4, c3)), inference(lemma,lemma(discharge,[]))).
% 0.97/0.95 tff(1674,plain,
% 0.97/0.95 (big_r(c2, f5(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1673, 431])).
% 0.97/0.95 tff(1675,plain,
% 0.97/0.95 ($false),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1668, 1561, 431, 442, 1539, 1674, 1658])).
% 0.97/0.95 tff(1676,plain,((~big_r(f5(c2), f6(c2))) | big_r(c4, c3)), inference(lemma,lemma(discharge,[]))).
% 0.97/0.95 tff(1677,plain,
% 0.97/0.95 (~big_r(f5(c2), f6(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1676, 431])).
% 0.97/0.95 tff(1678,plain,
% 0.97/0.95 (big_r(f5(c2), f6(c2)) | big_p(f2(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1549, 1635])).
% 0.97/0.95 tff(1679,plain,
% 0.97/0.95 (big_p(f2(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1678, 1677])).
% 0.97/0.95 tff(1680,plain,
% 0.97/0.95 (big_r(f1(c2), f2(c2)) | big_r(f5(c2), f6(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1557, 1635])).
% 0.97/0.95 tff(1681,plain,
% 0.97/0.95 (big_r(f1(c2), f2(c2))),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[1680, 1677])).
% 0.97/0.95 tff(1682,plain,
% 0.97/0.95 ($false),
% 0.97/0.95 inference(unit_resolution,[status(thm)],[448, 1561, 431, 442, 1671, 1681, 1679])).
% 0.97/0.95 tff(1683,plain,(big_r(c4, c3)), inference(lemma,lemma(discharge,[]))).
% 0.97/0.95 tff(1684,plain,
% 0.97/0.95 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f5(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f5(c4)))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1685,plain,
% 0.97/0.95 ((big_r(c4, f5(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> (big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f5(c4)))),
% 0.97/0.95 inference(rewrite,[status(thm)],[])).
% 0.97/0.95 tff(1686,plain,
% 0.97/0.95 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c4, f5(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f5(c4))))),
% 0.97/0.95 inference(monotonicity,[status(thm)],[1685])).
% 0.97/0.95 tff(1687,plain,
% 0.97/0.95 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c4, f5(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f5(c4)))),
% 0.97/0.95 inference(transitivity,[status(thm)],[1686, 1684])).
% 0.97/0.95 tff(1688,plain,
% 0.97/0.95 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c4, f5(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.97/0.96 inference(quant_inst,[status(thm)],[])).
% 0.97/0.96 tff(1689,plain,
% 0.97/0.96 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f5(c4))),
% 0.97/0.96 inference(modus_ponens,[status(thm)],[1688, 1687])).
% 0.97/0.96 tff(1690,plain,
% 0.97/0.96 (big_r(c2, f1(c2)) | (~big_p(c3)) | big_r(c4, f5(c4))),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[1689, 1030, 1635, 1683, 1244])).
% 0.97/0.96 tff(1691,plain,
% 0.97/0.96 (big_r(c4, f5(c4))),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[1690, 1650, 1])).
% 0.97/0.96 tff(1692,plain,
% 0.97/0.96 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f5(c4), f6(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f5(c4), f6(c4)))),
% 0.97/0.96 inference(rewrite,[status(thm)],[])).
% 0.97/0.96 tff(1693,plain,
% 0.97/0.96 ((big_r(f5(c4), f6(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> (big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f5(c4), f6(c4)))),
% 0.97/0.96 inference(rewrite,[status(thm)],[])).
% 0.97/0.96 tff(1694,plain,
% 0.97/0.96 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c4), f6(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f5(c4), f6(c4))))),
% 0.97/0.96 inference(monotonicity,[status(thm)],[1693])).
% 0.97/0.96 tff(1695,plain,
% 0.97/0.96 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c4), f6(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f5(c4), f6(c4)))),
% 0.97/0.96 inference(transitivity,[status(thm)],[1694, 1692])).
% 0.97/0.96 tff(1696,plain,
% 0.97/0.96 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c4), f6(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.97/0.96 inference(quant_inst,[status(thm)],[])).
% 0.97/0.96 tff(1697,plain,
% 0.97/0.96 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f5(c4), f6(c4))),
% 0.97/0.96 inference(modus_ponens,[status(thm)],[1696, 1695])).
% 0.97/0.96 tff(1698,plain,
% 0.97/0.96 (big_r(c2, f1(c2)) | (~big_p(c3)) | big_r(f5(c4), f6(c4))),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[1697, 1051, 1635, 1683, 1244])).
% 0.97/0.96 tff(1699,plain,
% 0.97/0.96 (big_r(f5(c4), f6(c4))),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[1698, 1650, 1])).
% 0.97/0.96 tff(1700,plain,
% 0.97/0.96 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f6(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f6(c4)))),
% 0.97/0.96 inference(rewrite,[status(thm)],[])).
% 0.97/0.96 tff(1701,plain,
% 0.97/0.96 ((big_p(f6(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> (big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f6(c4)))),
% 0.97/0.96 inference(rewrite,[status(thm)],[])).
% 0.97/0.96 tff(1702,plain,
% 0.97/0.96 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f6(c4))))),
% 0.97/0.96 inference(monotonicity,[status(thm)],[1701])).
% 0.97/0.96 tff(1703,plain,
% 0.97/0.96 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f6(c4)))),
% 0.97/0.96 inference(transitivity,[status(thm)],[1702, 1700])).
% 0.97/0.96 tff(1704,plain,
% 0.97/0.96 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.97/0.96 inference(quant_inst,[status(thm)],[])).
% 0.97/0.96 tff(1705,plain,
% 0.97/0.96 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_p(c1)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f6(c4))),
% 0.97/0.96 inference(modus_ponens,[status(thm)],[1704, 1703])).
% 0.97/0.96 tff(1706,plain,
% 0.97/0.96 (big_r(c2, f1(c2)) | (~big_p(c3)) | big_p(f6(c4))),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[1705, 1009, 1635, 1683, 1244])).
% 0.97/0.96 tff(1707,plain,
% 0.97/0.96 (big_p(f6(c4))),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[1706, 1650, 1])).
% 0.97/0.96 tff(1708,plain,
% 0.97/0.96 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.97/0.96 inference(rewrite,[status(thm)],[])).
% 0.97/0.96 tff(1709,plain,
% 0.97/0.96 (((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2)))) <=> ((~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.97/0.96 inference(rewrite,[status(thm)],[])).
% 0.97/0.96 tff(1710,plain,
% 0.97/0.96 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2)))))),
% 0.97/0.96 inference(monotonicity,[status(thm)],[1709])).
% 0.97/0.96 tff(1711,plain,
% 0.97/0.96 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))))),
% 0.97/0.96 inference(transitivity,[status(thm)],[1710, 1708])).
% 0.97/0.96 tff(1712,plain,
% 0.97/0.96 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))),
% 0.97/0.96 inference(quant_inst,[status(thm)],[])).
% 0.97/0.96 tff(1713,plain,
% 0.97/0.96 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2)))),
% 0.97/0.96 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 0.97/0.96 tff(1714,plain,
% 0.97/0.96 ($false),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[1713, 196, 1707, 1641, 1639, 1637, 1699, 1691])).
% 0.97/0.96 tff(1715,plain,(big_r(c2, f1(c2))), inference(lemma,lemma(discharge,[]))).
% 0.97/0.96 tff(1716,assumption,(big_r(c2, f1(c2))), introduced(assumption)).
% 0.97/0.96 tff(1717,plain,
% 0.97/0.96 ($false),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[491, 472, 1561, 485, 1716, 1654, 1652])).
% 0.97/0.96 tff(1718,plain,(big_p(f6(c2)) | big_p(c3) | (~big_r(c2, f1(c2)))), inference(lemma,lemma(discharge,[]))).
% 0.97/0.96 tff(1719,plain,
% 0.97/0.96 (big_p(f6(c2))),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[1718, 472, 1716])).
% 0.97/0.96 tff(1720,plain,
% 0.97/0.96 (~big_r(f5(c2), f6(c2))),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[1649, 472, 1538, 1719])).
% 0.97/0.96 tff(1721,plain,
% 0.97/0.96 (big_p(f2(c2))),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[1678, 1720])).
% 0.97/0.96 tff(1722,plain,
% 0.97/0.96 (big_r(f1(c2), f2(c2))),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[1680, 1720])).
% 0.97/0.96 tff(1723,plain,
% 0.97/0.96 ($false),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[491, 472, 1561, 485, 1716, 1722, 1721])).
% 0.97/0.96 tff(1724,plain,(big_p(c3) | (~big_r(c2, f1(c2))) | (~big_r(c2, f5(c2)))), inference(lemma,lemma(discharge,[]))).
% 0.97/0.96 tff(1725,plain,
% 0.97/0.96 (~big_r(c2, f5(c2))),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[1724, 472, 1715])).
% 0.97/0.96 tff(1726,plain,
% 0.97/0.96 (big_p(f2(c2))),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[1659, 1725])).
% 0.97/0.96 tff(1727,plain,
% 0.97/0.96 (big_r(f1(c2), f2(c2))),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[1661, 1725])).
% 0.97/0.96 tff(1728,plain,
% 0.97/0.96 ($false),
% 0.97/0.96 inference(unit_resolution,[status(thm)],[491, 472, 1561, 485, 1715, 1727, 1726])).
% 0.97/0.96 tff(1729,plain,(big_p(c3)), inference(lemma,lemma(discharge,[]))).
% 1.00/0.96 tff(1730,plain,
% 1.00/0.96 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 1.00/0.96 inference(rewrite,[status(thm)],[])).
% 1.00/0.96 tff(1731,plain,
% 1.00/0.96 ((big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 1.00/0.96 inference(rewrite,[status(thm)],[])).
% 1.00/0.96 tff(1732,plain,
% 1.00/0.96 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4))))),
% 1.00/0.96 inference(monotonicity,[status(thm)],[1731])).
% 1.00/0.96 tff(1733,plain,
% 1.00/0.96 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 1.00/0.96 inference(transitivity,[status(thm)],[1732, 1730])).
% 1.00/0.96 tff(1734,plain,
% 1.00/0.96 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 1.00/0.96 inference(quant_inst,[status(thm)],[])).
% 1.00/0.96 tff(1735,plain,
% 1.00/0.96 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4))),
% 1.00/0.96 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 1.00/0.96 tff(1736,plain,
% 1.00/0.96 ((~big_p(c3)) | big_p(f6(c2)) | big_r(f1(c4), f2(c4))),
% 1.00/0.96 inference(unit_resolution,[status(thm)],[1735, 942, 1635, 1683, 1244])).
% 1.00/0.96 tff(1737,plain,
% 1.00/0.96 (big_r(f1(c4), f2(c4))),
% 1.00/0.96 inference(unit_resolution,[status(thm)],[1736, 1460, 1729])).
% 1.00/0.96 tff(1738,plain,
% 1.00/0.96 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 1.00/0.96 inference(rewrite,[status(thm)],[])).
% 1.00/0.96 tff(1739,plain,
% 1.00/0.96 ((big_p(f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 1.00/0.96 inference(rewrite,[status(thm)],[])).
% 1.00/0.96 tff(1740,plain,
% 1.00/0.96 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4))))),
% 1.00/0.96 inference(monotonicity,[status(thm)],[1739])).
% 1.00/0.96 tff(1741,plain,
% 1.00/0.96 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 1.00/0.96 inference(transitivity,[status(thm)],[1740, 1738])).
% 1.00/0.96 tff(1742,plain,
% 1.00/0.96 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 1.00/0.96 inference(quant_inst,[status(thm)],[])).
% 1.00/0.96 tff(1743,plain,
% 1.00/0.96 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4))),
% 1.00/0.96 inference(modus_ponens,[status(thm)],[1742, 1741])).
% 1.00/0.96 tff(1744,plain,
% 1.00/0.96 ((~big_p(c3)) | big_p(f6(c2)) | big_p(f2(c4))),
% 1.00/0.96 inference(unit_resolution,[status(thm)],[1743, 873, 1635, 1683, 1244])).
% 1.00/0.96 tff(1745,plain,
% 1.00/0.96 (big_p(f2(c4))),
% 1.00/0.96 inference(unit_resolution,[status(thm)],[1744, 1460, 1729])).
% 1.00/0.96 tff(1746,plain,
% 1.00/0.96 ((~big_p(c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4))),
% 1.00/0.96 inference(unit_resolution,[status(thm)],[1036, 1030, 1683])).
% 1.00/0.96 tff(1747,plain,
% 1.00/0.96 (big_r(c4, f5(c4))),
% 1.00/0.96 inference(unit_resolution,[status(thm)],[1746, 1650, 3])).
% 1.00/0.96 tff(1748,plain,
% 1.00/0.96 ((~big_p(c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4))),
% 1.00/0.96 inference(unit_resolution,[status(thm)],[1057, 1051, 1683])).
% 1.00/0.96 tff(1749,plain,
% 1.00/0.96 (big_r(f5(c4), f6(c4))),
% 1.00/0.96 inference(unit_resolution,[status(thm)],[1748, 1650, 3])).
% 1.00/0.96 tff(1750,plain,
% 1.00/0.96 ((~big_p(c3)) | big_r(c4, f1(c4)) | big_p(f6(c4))),
% 1.00/0.96 inference(unit_resolution,[status(thm)],[1015, 1009, 1683])).
% 1.00/0.96 tff(1751,plain,
% 1.00/0.96 (big_p(f6(c4))),
% 1.00/0.96 inference(unit_resolution,[status(thm)],[1750, 1650, 3])).
% 1.00/0.96 tff(1752,plain,
% 1.00/0.96 ($false),
% 1.00/0.96 inference(unit_resolution,[status(thm)],[1713, 196, 1751, 1641, 1639, 1637, 1749, 1747])).
% 1.00/0.96 tff(1753,plain,(big_r(c2, f1(c2)) | big_r(c4, f1(c4))), inference(lemma,lemma(discharge,[]))).
% 1.00/0.96 tff(1754,plain,
% 1.00/0.96 (big_r(c2, f1(c2))),
% 1.00/0.96 inference(unit_resolution,[status(thm)],[1753, 3])).
% 1.00/0.96 tff(1755,plain,
% 1.00/0.96 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 1.00/0.96 inference(rewrite,[status(thm)],[])).
% 1.00/0.96 tff(1756,plain,
% 1.00/0.96 ((big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 1.00/0.96 inference(rewrite,[status(thm)],[])).
% 1.00/0.96 tff(1757,plain,
% 1.00/0.96 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4))))),
% 1.00/0.97 inference(monotonicity,[status(thm)],[1756])).
% 1.00/0.97 tff(1758,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 1.00/0.97 inference(transitivity,[status(thm)],[1757, 1755])).
% 1.00/0.97 tff(1759,plain,
% 1.00/0.97 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 1.00/0.97 inference(quant_inst,[status(thm)],[])).
% 1.00/0.97 tff(1760,plain,
% 1.00/0.97 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4))),
% 1.00/0.97 inference(modus_ponens,[status(thm)],[1759, 1758])).
% 1.00/0.97 tff(1761,plain,
% 1.00/0.97 ((~big_p(c3)) | big_r(c2, f5(c2)) | big_r(c4, f1(c4))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1760, 1030, 1635, 1683, 1244])).
% 1.00/0.97 tff(1762,plain,
% 1.00/0.97 (~big_p(c3)),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1761, 1488, 3])).
% 1.00/0.97 tff(1763,plain,
% 1.00/0.97 ($false),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[491, 1762, 1561, 485, 1716, 1662, 1660])).
% 1.00/0.97 tff(1764,plain,(big_r(c2, f5(c2)) | (~big_r(c2, f1(c2))) | big_r(c4, f1(c4))), inference(lemma,lemma(discharge,[]))).
% 1.00/0.97 tff(1765,plain,
% 1.00/0.97 (big_r(c2, f5(c2))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1764, 1754, 3])).
% 1.00/0.97 tff(1766,plain,
% 1.00/0.97 (big_p(c3)),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1724, 1754, 1765])).
% 1.00/0.97 tff(1767,plain,
% 1.00/0.97 (big_r(c4, f5(c4))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1746, 1766, 3])).
% 1.00/0.97 tff(1768,plain,
% 1.00/0.97 (big_r(f5(c4), f6(c4))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1748, 1766, 3])).
% 1.00/0.97 tff(1769,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 1.00/0.97 inference(rewrite,[status(thm)],[])).
% 1.00/0.97 tff(1770,plain,
% 1.00/0.97 ((big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 1.00/0.97 inference(rewrite,[status(thm)],[])).
% 1.00/0.97 tff(1771,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4))))),
% 1.00/0.97 inference(monotonicity,[status(thm)],[1770])).
% 1.00/0.97 tff(1772,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 1.00/0.97 inference(transitivity,[status(thm)],[1771, 1769])).
% 1.00/0.97 tff(1773,plain,
% 1.00/0.97 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 1.00/0.97 inference(quant_inst,[status(thm)],[])).
% 1.00/0.97 tff(1774,plain,
% 1.00/0.97 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4))),
% 1.00/0.97 inference(modus_ponens,[status(thm)],[1773, 1772])).
% 1.00/0.97 tff(1775,plain,
% 1.00/0.97 ((~big_p(c3)) | big_p(f6(c2)) | big_r(c4, f1(c4))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1774, 1009, 1635, 1683, 1244])).
% 1.00/0.97 tff(1776,plain,
% 1.00/0.97 (big_p(f6(c2))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1775, 1766, 3])).
% 1.00/0.97 tff(1777,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 1.00/0.97 inference(rewrite,[status(thm)],[])).
% 1.00/0.97 tff(1778,plain,
% 1.00/0.97 ((big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 1.00/0.97 inference(rewrite,[status(thm)],[])).
% 1.00/0.97 tff(1779,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4))))),
% 1.00/0.97 inference(monotonicity,[status(thm)],[1778])).
% 1.00/0.97 tff(1780,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4)))),
% 1.00/0.97 inference(transitivity,[status(thm)],[1779, 1777])).
% 1.00/0.97 tff(1781,plain,
% 1.00/0.97 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 1.00/0.97 inference(quant_inst,[status(thm)],[])).
% 1.00/0.97 tff(1782,plain,
% 1.00/0.97 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(c4, f1(c4))),
% 1.00/0.97 inference(modus_ponens,[status(thm)],[1781, 1780])).
% 1.00/0.97 tff(1783,plain,
% 1.00/0.97 ((~big_p(c3)) | big_r(f5(c2), f6(c2)) | big_r(c4, f1(c4))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1782, 1051, 1635, 1683, 1244])).
% 1.00/0.97 tff(1784,plain,
% 1.00/0.97 (big_r(f5(c2), f6(c2))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1783, 1766, 3])).
% 1.00/0.97 tff(1785,plain,
% 1.00/0.97 (big_p(f6(c4))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1750, 1766, 3])).
% 1.00/0.97 tff(1786,plain,
% 1.00/0.97 ($false),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1713, 196, 1785, 1784, 1765, 1776, 1768, 1767])).
% 1.00/0.97 tff(1787,plain,(big_r(c4, f1(c4))), inference(lemma,lemma(discharge,[]))).
% 1.00/0.97 tff(1788,plain,
% 1.00/0.97 (big_p(f6(c2)) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_p(f2(c4)))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1534, 1635])).
% 1.00/0.97 tff(1789,plain,
% 1.00/0.97 (big_p(f6(c2)) | (~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4)))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1788, 1787])).
% 1.00/0.97 tff(1790,plain,
% 1.00/0.97 ($false),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1789, 1745, 1460, 1737])).
% 1.00/0.97 tff(1791,plain,(big_p(f6(c2))), inference(lemma,lemma(discharge,[]))).
% 1.00/0.97 tff(1792,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 1.00/0.97 inference(rewrite,[status(thm)],[])).
% 1.00/0.97 tff(1793,plain,
% 1.00/0.97 ((big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 1.00/0.97 inference(rewrite,[status(thm)],[])).
% 1.00/0.97 tff(1794,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4))))),
% 1.00/0.97 inference(monotonicity,[status(thm)],[1793])).
% 1.00/0.97 tff(1795,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 1.00/0.97 inference(transitivity,[status(thm)],[1794, 1792])).
% 1.00/0.97 tff(1796,plain,
% 1.00/0.97 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 1.00/0.97 inference(quant_inst,[status(thm)],[])).
% 1.00/0.97 tff(1797,plain,
% 1.00/0.97 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4))),
% 1.00/0.97 inference(modus_ponens,[status(thm)],[1796, 1795])).
% 1.00/0.97 tff(1798,plain,
% 1.00/0.97 ((~big_p(c3)) | big_r(c2, f5(c2)) | big_r(f1(c4), f2(c4))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1797, 963, 1635, 1683, 1244])).
% 1.00/0.97 tff(1799,plain,
% 1.00/0.97 (big_r(f1(c4), f2(c4))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1798, 1488, 1729])).
% 1.00/0.97 tff(1800,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 1.00/0.97 inference(rewrite,[status(thm)],[])).
% 1.00/0.97 tff(1801,plain,
% 1.00/0.97 ((big_r(c2, f5(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 1.00/0.97 inference(rewrite,[status(thm)],[])).
% 1.00/0.97 tff(1802,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f5(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4))))),
% 1.00/0.97 inference(monotonicity,[status(thm)],[1801])).
% 1.00/0.97 tff(1803,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f5(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 1.00/0.97 inference(transitivity,[status(thm)],[1802, 1800])).
% 1.00/0.97 tff(1804,plain,
% 1.00/0.97 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(c2, f5(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 1.00/0.97 inference(quant_inst,[status(thm)],[])).
% 1.00/0.97 tff(1805,plain,
% 1.00/0.97 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4))),
% 1.00/0.97 inference(modus_ponens,[status(thm)],[1804, 1803])).
% 1.00/0.97 tff(1806,plain,
% 1.00/0.97 ((~big_p(c3)) | big_r(c2, f5(c2)) | big_p(f2(c4))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1805, 894, 1635, 1683, 1244])).
% 1.00/0.97 tff(1807,plain,
% 1.00/0.97 (big_p(f2(c4))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1806, 1488, 1729])).
% 1.00/0.97 tff(1808,plain,
% 1.00/0.97 (big_r(c2, f5(c2)) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_p(f2(c4)))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1514, 1635])).
% 1.00/0.97 tff(1809,plain,
% 1.00/0.97 (big_r(c2, f5(c2)) | (~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4)))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1808, 1787])).
% 1.00/0.97 tff(1810,plain,
% 1.00/0.97 ($false),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1809, 1807, 1799, 1488])).
% 1.00/0.97 tff(1811,plain,(big_r(c2, f5(c2))), inference(lemma,lemma(discharge,[]))).
% 1.00/0.97 tff(1812,assumption,(~big_r(f5(c2), f6(c2))), introduced(assumption)).
% 1.00/0.97 tff(1813,plain,
% 1.00/0.97 (big_p(f2(c2))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1678, 1812])).
% 1.00/0.97 tff(1814,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 1.00/0.97 inference(rewrite,[status(thm)],[])).
% 1.00/0.97 tff(1815,plain,
% 1.00/0.97 ((big_r(f5(c2), f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 1.00/0.97 inference(rewrite,[status(thm)],[])).
% 1.00/0.97 tff(1816,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c2), f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4))))),
% 1.00/0.97 inference(monotonicity,[status(thm)],[1815])).
% 1.00/0.97 tff(1817,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c2), f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4)))),
% 1.00/0.97 inference(transitivity,[status(thm)],[1816, 1814])).
% 1.00/0.97 tff(1818,plain,
% 1.00/0.97 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (big_r(f5(c2), f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 1.00/0.97 inference(quant_inst,[status(thm)],[])).
% 1.00/0.97 tff(1819,plain,
% 1.00/0.97 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_p(f2(c4))),
% 1.00/0.97 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 1.00/0.97 tff(1820,plain,
% 1.00/0.97 ((~big_p(c3)) | big_r(f5(c2), f6(c2)) | big_p(f2(c4))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1819, 915, 1635, 1683, 1244])).
% 1.00/0.97 tff(1821,plain,
% 1.00/0.97 (big_p(f2(c4))),
% 1.00/0.97 inference(unit_resolution,[status(thm)],[1820, 1812, 1729])).
% 1.00/0.97 tff(1822,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 1.00/0.97 inference(rewrite,[status(thm)],[])).
% 1.00/0.97 tff(1823,plain,
% 1.00/0.97 ((big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 1.00/0.97 inference(rewrite,[status(thm)],[])).
% 1.00/0.97 tff(1824,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4))))),
% 1.00/0.97 inference(monotonicity,[status(thm)],[1823])).
% 1.00/0.97 tff(1825,plain,
% 1.00/0.97 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4)))),
% 1.00/0.98 inference(transitivity,[status(thm)],[1824, 1822])).
% 1.00/0.98 tff(1826,plain,
% 1.00/0.98 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 1.00/0.98 inference(quant_inst,[status(thm)],[])).
% 1.00/0.98 tff(1827,plain,
% 1.00/0.98 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : (big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(c3)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_r(c2, c1)) | big_r(f1(c4), f2(c4))),
% 1.00/0.98 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 1.00/0.98 tff(1828,plain,
% 1.00/0.98 ((~big_p(c3)) | big_r(f5(c2), f6(c2)) | big_r(f1(c4), f2(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[1827, 984, 1635, 1683, 1244])).
% 1.00/0.98 tff(1829,plain,
% 1.00/0.98 (big_r(f1(c4), f2(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[1828, 1812, 1729])).
% 1.00/0.98 tff(1830,plain,
% 1.00/0.98 (big_r(f1(c2), f2(c2))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[1680, 1812])).
% 1.00/0.98 tff(1831,plain,
% 1.00/0.98 ($false),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[226, 196, 1715, 1830, 1829, 1787, 1821, 1813])).
% 1.00/0.98 tff(1832,plain,(big_r(f5(c2), f6(c2))), inference(lemma,lemma(discharge,[]))).
% 1.00/0.98 tff(1833,plain,
% 1.00/0.98 ((~big_p(c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[969, 963, 1683])).
% 1.00/0.98 tff(1834,plain,
% 1.00/0.98 (big_r(c4, f5(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[1833, 258, 1729])).
% 1.00/0.98 tff(1835,plain,
% 1.00/0.98 ((~big_p(c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[990, 984, 1683])).
% 1.00/0.98 tff(1836,plain,
% 1.00/0.98 (big_r(f5(c4), f6(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[1835, 258, 1729])).
% 1.00/0.98 tff(1837,plain,
% 1.00/0.98 ((~big_p(c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[948, 942, 1683])).
% 1.00/0.98 tff(1838,plain,
% 1.00/0.98 (big_p(f6(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[1837, 258, 1729])).
% 1.00/0.98 tff(1839,plain,
% 1.00/0.98 ($false),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[1713, 196, 1838, 1832, 1811, 1791, 1836, 1834])).
% 1.00/0.98 tff(1840,plain,(big_r(f1(c4), f2(c4))), inference(lemma,lemma(discharge,[]))).
% 1.00/0.98 tff(1841,plain,
% 1.00/0.98 ((~big_r(f5(c2), f6(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2)))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[1541, 1787])).
% 1.00/0.98 tff(1842,plain,
% 1.00/0.98 (~big_p(f2(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[1841, 1840, 1832, 1811, 1791])).
% 1.00/0.98 tff(1843,plain,
% 1.00/0.98 ((~big_p(c3)) | big_r(c4, f5(c4)) | big_p(f2(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[900, 894, 1683])).
% 1.00/0.98 tff(1844,plain,
% 1.00/0.98 (big_r(c4, f5(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[1843, 1842, 1729])).
% 1.00/0.98 tff(1845,plain,
% 1.00/0.98 ((~big_p(c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[921, 915, 1683])).
% 1.00/0.98 tff(1846,plain,
% 1.00/0.98 (big_r(f5(c4), f6(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[1845, 1842, 1729])).
% 1.00/0.98 tff(1847,plain,
% 1.00/0.98 ((~big_p(c3)) | big_p(f6(c4)) | big_p(f2(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[879, 873, 1683])).
% 1.00/0.98 tff(1848,plain,
% 1.00/0.98 (big_p(f6(c4))),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[1847, 1842, 1729])).
% 1.00/0.98 tff(1849,plain,
% 1.00/0.98 ($false),
% 1.00/0.98 inference(unit_resolution,[status(thm)],[1713, 196, 1848, 1832, 1811, 1791, 1846, 1844])).
% 1.00/0.98 % SZS output end Proof
%------------------------------------------------------------------------------